First of all, who's unemployed?
This depends on the kind of creatures that exist in your world. Specifically, it depends on what these creatures are better at than the humans living in the unemployment-ridden kingdom.
Labourers:
You've already established that there are golems in the world, that are (presumably) stronger and more endurable than humans, and therefore they outcompete humans in the manual labour section. So, laborers will have higher rates of unemployment.
Scholars:
Are there creatures smarter than humans? If so, how much smarter? Do these creatures have societies of their own? These three questions are essential in finding out whether scholars, and the like, will be unemployed. I find it hard to believe creatures vastly smarter than humans would bother to be employed as scholars for humans, if they have their own society. In this event, they'd either ignore humans, sell knowledge to them or be hostile towards them. However, why the heck would they bother to work for humans, trying to help them solve questions they're forefathers figured out long ago?
If they don't have their own societies, then they might want to work for humans in order to have a place to stay, and maybe, something to do. However, why wouldn't they have their own society? I can think of two reasons:
(1) They're nearly extinct, and thus their past societies are gone, and they're too few to form new ones.
(2) They're anti- or asocial creatures, and thus never formed societies.
In the first case, then they wouldn't affect the unemployment rates of scholars that much, since there's less of them to outcompete humans. In the second case, they'd probably not want to work for humans. However, from an evolutionary standpoint, it's unlikely they'd become so smart if they're inherently anti- or asocial.
What if they're forced into working for humans, through magical or other means? Well, given their intelligence, I think they'd probably be able to remain outside of the captive of comparably dumb humans. However, let's say they don't possess magical abilities; then, humans may be able to hold them captive and work for them.
Another possibility is that these creatures aren't that smart, meaning they're smart enough to enslave for scholarly work, but not smart enough to evade/escape this enslavement. However, I'd say this too would require them to be without a society. If there was a society of these smart creatures (one probably more advanced than human societies), then they'd probably not allow humans to enslave their kind.
So, this leaves us with three cases for when it makes sense that scholars would be experiencing heightened rates of unemployment:
(1) There are smart creatures that for some reason are willing to work as scholars for humans.
(2) There are creatures smarter than humans, but not smart enough to evade/escape their enslavement.
(3) There are smart creatures that don't posess magical powers, being magically enslaved by humans and forced to do scholarly work.
Cases (1) and (2) probably require the creatures to be without a society. Case (3) would require the government to allow for the enslavement of conscious beings. Not sure if the "no authoriatarian/totalitarian" clause is a product of plot necessity or a product of the government being somewhat similar to modern morals, but if the latter, it is unlikely that the enslavement of such beings would be okay. In that case, it would have to be an illegal, hidden practice, which would be hard to pull off given that the scholars would often need to do observational work out in the world. In this case, due to the decreased utility of illegal enslavement, that's additionally hard to hide due to the nature of the work, these creatures' effect on unemployment rates would be lower.
Servants:
Basically, servers, babysitters, etc. People in non-scholarly lines of work that aren't primarily characterized by manual labour. Golems would not outcompete these people, as you wouldn't have a hulking golem serving your wine, would you? Furthermore, any creatures that look scary, would not be favorable for jobs involving social interactions. So, if there are any employable/enslavable creatures in your world that conform to these restrictions, and if they're better at the job than humans, and/or are cheaper to employ/enslave, then this would leave more humans unemployed.
So, how to alleviate or stop the unemployment?
Let's look at the solutions case by case. I'm assuming the perspective of the king here.
Labourers:
Invest in tools, making them better, but also harder to use for non-humans. If golems are dumber than humans, then making more complex tools could achieve this. Otherwise, I think golems are probably not the most dexterous creatures, so creating tools requiring high dexterity would also achieve this. However, doing this successfully would make unemployment rates heighten for golems. I assume the king is concerned with the unemployment of humans.
Scholars:
A solution possible if these smart creatures are an endangered species; commit genocide, driving them into extinction, or driving them away. Other ways to drive them away would be to install and cultivate systemic and cultural discrimination of, and racism towards, the smart creatures, making their lives within human civilization terrible. Given that their superior intelligence might make a lot of humans envious and make them hard to understand for a lot of humans, causing further resentment and lots of conflicts due to misunderstandings, as well as a lower empathy due to diminished social interaction, I think this kind of racism might just evolve on its own.
However, what if these creatures are enslaved and not extinct? Then they don't have the ability to leave the human societies, and extinction via genocide isn't realistic. In the event that this enslavement is illegal, the king could just allocate a lot of resources to apprehending the slavers and freeing the slaves. Given how smart these creatures are, this task could probably be benefitted a lot by asking the freed slaves to help, which they'd likely want to do (unless they're anti- or asocial). Then, after having freed them all, the king kindly tells them they cannot stay in his kingdom (given that he wants to alleviate the unemployment rates), or, he could find something else for them to do.
Given that in this case, the smart creatures aren't extinct, they probably have societies (given they're not anti- or asocial, as said). So, the king could also gain resources and help from those societies as well.
Servants:
Here, the same kind of solutions as mentioned above could apply. Genocide, the cultivation of discrimination and racism of/against the creatures, or stopping the enslavement of the creatures.
Solution that applies to all three occupational groups
The king could allocate lots of resources to the education and training of humans, so as to make them as good, or better, than their non-human competitors.
The king could also pass various laws and taxes that makes practices leaving humans unemployed harder or impossible to maintain.
Notes:
I want to say that in the case of human scholars being outcompeted by smarter non-humans, I think the benefits would be greater than the downsides. If they're really smart, their contributions would propel the kingdom's science and technology far ahead, which would in turn create new jobs and new areas of study, thus alleviating the unemployment. Also, the advances in tech and science may just solve the problems of unemployment, making it a non-issue in the first place.
Furthermore, I'm not sure that these smarter creatures would even cause a lot of unemployment in scholars. In a kingdom, I'd think a lot of scholarly work is done independently, by more wealthy individuals, or as service to the king/church. The latter means that the king can limit the unemployment of humans by not hiring the non-humans for studies funded by the crown. If the church is under the king's control, this applies to that as well.
As for the former, just because a few smart non-humans are publishing more interesting, better, and more relevant work, doesn't mean that these self-employed, human scholars still won't make a living. There's countless of things that need to be studied, and if these creatures are an endangered species, they can't cover it all. Furthermore, if they're so smart, they're likely to be more occupied with harder topics and questions, leaving lots of less complex stuff for humans to study and publish on. That less complex stuff will also be more digestible to humans, meaning it may have a greater appeal as well.