- By post-scarcity in this case, I mean that the entire society's sustenance and basic comfort level needs can be met through the minimal effort of what modern man would consider hobbies and odds-and-ends work.
- These people live in towns and cities of sizes that were typical in the medieval world.
- These people have technology on par with the medieval world, but things that would have only been available to the middle and upper classes are universally available here.
- They live on an alien world; so, made-up flora, fauna, and environmental factors are fine as long as they can be scientifically justified.
- These people are originally from Earth. They evolved from an early human ancestor such as homo erectus which was transported to this alien world between 500,000 and 2,000,000 years ago.
- These people do not enslave another intelligent species to meet their needs for them.
These people have technology on par with the medieval world.
Medieval technology could ensure food as long as there was no obstacle. The first frost, hail or drought out of season would mean famine, and that was the case until very recent times, if not even until today in part of the world.
I dare to say that medieval technology is the embodiment of scarcity.
So, no, I don't think post-scarcity would be possible in a medieval world.
Living in basic sustenance & comfort means access to :
- Food & water
All those things, even with today technology, need work, lots of it. And in towns, it's even worse : the water sources, the fields, the animals, the timber and the stones are further away than for a peasant.
You need something that provide for all those things. For example, you have post scarcity for a master class with servants of a kind or another.
You need material and product that are easy to harvest and use, so that work isn't too hard and leave a lot of free time.
Some examples :
- a kind of giant snail that can be eaten and with a big enough shell to live within
- A fast growing crop that can be grown on flat roofs and harvested on a regular base so that one missed harvest is not that important
- a tree with a tender wood, easy to cut, that dry really hard
Firstly I suggest that an alien planet capable of supporting human life would in all likelihood also be home to an alien biosphere from an alien biogenesis with completely different biochemistry. Any such life would be very well adapted to the environment on that planet (unlike incoming Earth based life forms). It would also be difficult to eradicate, at the very best inedible and at worst highly toxic.
Setting that to one side (perhaps life on the planet was still in the oceans) and assuming Terrestrial life has successfully colonised the land surface, a lot would depend on the nature of the society and the climate. One key element would be some form of effective population control. If this was not possible then the population would be doomed to boom and bust feast and famine cyclically on a long enough time span. But if there was some means of keeping the population at roughly the same level then there would be hope.
Another problem would be human nature and the tendency to form hierarchies governed by an elite. This is present in all human societies and has lead to huge inequality within those societies with the kings, lords, chiefs and similar taking the lion’s share of any surplus. This would have to be prevented by some means.
Finally there would need to be a benign climate (much better than northern Europe). There are some areas on Earth where the weather is warm all year round and there is plentiful rainfall. In such locations it is possible to get two harvests every year. With the correct mix of crops and the absence of pests and diseases any population should have a bountiful supply of food.
Permaculture and the Periodic Apocalypse
For "Post Scarcity" you need food production to basically take care of itself. In the Medieval world the vast majority of people were involved in farming. So cover your alien planet with fruit and nut trees that provide limited value to the local fauna, but that are just perfect for people.
Basically, money DOES grow on trees - so we're post scarcity.
Then Population Explodes
The problem is, of course, that without famine or war to control population, the population is going to grow rapidly. Urbanization will occur.
Dense urban populations with free time will lead to universities, explorers clubs, and the general advancement of knowledge. You will rapidly exit the Medieval tech level. So you need to keep the population low.
Enter the Apocalypse
You need some kind of periodic mass death to prevent people from advancing technologically. Bonus points if your apocalypse targets urban centers, since that's where the exchange of ideas really heats up.
Possible inspirations include:
- Dragons - Large Monsters are known to attack population centers 
- Plagues - COVID certainly is hitting urban areas harder, and a highly virulent illness could exist in rare animals, only affecting humans when the population is large enough that the host's territory is impacted.
- Long Period Famines - maybe there's something that lowers the productivity of the vital money trees, but only at very long intervals. Every 200 years, the trees cease production for a year, all at once. (Maybe there's something odd with the host star that lowers solar output?) It's so infrequent that the famine falls into myth before the next cycle hits.
In any case, the recipe for post-scarcity Mevdieval aliens is: easy access to food and something that keeps population density low.
To keep them from moving out of the Medieval era, you need something that prevents rising returns to human capital as people branch out into industrious pursuits.
To make that society post-scarcity, you need something that brings about a lot of stability for basic resources like food.
One good starting place to think about this might be The Potato's Contribution to Population and Urbanization: Evidence From A Historical Experiment by Nunn and Qian (2011). In it, they attempt to show that the spread of the potato out of central America "accounts for approximately one-quarter of the growth in Old World population and urbanization between 1700 and 1900."
This suggests to me that you could introduce a similar staple crop on your planet, but perhaps one that doesn't lend itself to large-scale farming. Combined with a very stable climate that lacks droughts, floods, and pests (or perhaps has them but the staple crop is resilient to them), you might be able to make this work. Something like a crop that needs a lot of space to grow, and is delicate and messy in a way that prevents automation - like things we still hand-pick today. Or imagine cotton before the invention of the cotton gin.
It would be hard to free up labor from farming to pursue other things. But as long as that labor was engaged in farming, everyone had plenty to eat. That would also help prevent people from dedicating their time to lots of education, thereby coming up with advanced things that will reduce the dependency on farming and break them out of the Medieval era.
That still leaves the problem of population though. Eventually, with enough people, land would become scarce and ruin your setup. I feel like you could hand-wave that away easily enough. Maybe the environment lowers birthrates such that it's very hard for the natives to grow the birth rate beyond the mortality rate. Happy coincidence; women are just fertile enough and the people just healthy enough that their population growth is checked at a nice equilibrium! Most models of macroeconomic growth also include population growth as an element of economic growth, so this might also help with your Medieval stagnation.
Another problem might be why people don't enslave others to do the work for them, such as in the cotton example. There are plenty of cultural ways you could explain this though. Maybe they're fiercely independent, and nothing motivates them to violent uprisings like taking away other's freedoms.
Anyway, there are lots of details you could tweak to accomplish this, but I feel like it has to start with a staple source of food that they can't easily mechanize production of.
In the long term probably no, evolution would find something that can compete with humans for resources (weeds).
However if the colonisation could have happened much more recently, say 500 years ago you could steal a planet from the book starship troopers. In the book they have found this world that has not harbored life on land that long. All that grow naturally is some primitive moss or such. That means that their crops from earth rapidly take over the ecosystem creating fields of food with no competition. This coupled with a very stable star and climate makes for easy living.
The Issue with Post-Scarcity here is population growth
This isn't as much of a danger for modern post-scarcity societies, as birth rates are far lower in modern societies (as in, people have control over how many children they have). In medieval times, birth rates were completely uncontrolled; due to high infant mortality, starvation and other issues, this was a relatively small problem.
However, if you take a medieval society and make it post-scarcity (putting aside for a moment the fact that you just took the jobs away from 80% of the population), this becomes an issue; improved health and reduced disease (I assume there would be less disease in the society you describe) means that most children will survive to adulthood, and with every couple having 5+ children, in only a few generations, population will explode. If we assume each generation is double the size of the one previous, in 500 years the population will have multiplied by a million, and done so again in another 500. Regardless of how abundant food is, this will quickly become an issue.
Of course, as I alluded earlier, medieval society is almost completely geared towards making food, whether cheap food for commoners or meat and pastries for wealthier folk. With this a non-issue, suddenly everyone's twiddling their thumbs. We've recently seen a smaller version of the effects this would have in America; bored and stir-crazy people riot and cause widespread mayhem over issues that would never have normally triggered such a large reaction. America has modern entertainment such as video games and movies, meaning that this would orders of magnitudes worse if you took away the jobs of the majority of the population when they have nothing else to do.