Start by thinking like your first generation of survivors
In the middle of the chaos, what is everyone focused on? In the days immediately after things settle down? In the months that stretch to years?
Your first and biggest concern will be safety. This means first aid, shelter/construction, self-defense from raiders, and food. If your original group of survivors lived in a religious region, then religion would certainly be preserved and possibly even elevated to a more central role in their society as well.
Everything that doesn't immediately feed into survival is now a luxury. A luxury that no one can afford. Anything that requires national or international scale manufacturing / refinement processes is a luxury that no one can afford. Anything that requires massive resources to bring about? Gone.
It won't be until later, after everyone is sure that the panic-phase of chaos is over, that they'll wish they'd taken more time to hoard technical books. Or download how-to guides to their portable devices before the internet went dark (and then print them out before the paper and ink run out).
But it will probably be too late for entire swaths of things we take for granted. Survival will have meant running, not carefully plotting out the future actions needed to keep technology working.
Extrapolate up from there
Medicine
So based on that, emergency medicine will stick around. Not all medicine though. Cancer treatment, or treatments for any of a thousand different chronic illnesses will probably be lost. No one will care how to produce insulin or any of a thousand drugs that are hard to reproduce without a vast manufacturing system. But drugs like penicillin might stick around. Or drugs that are reasonably easy to make from the resources at hand (natural extracts, etc.).
First aid, bone-setting, the need for cleanliness, those are all likely to survive.
Agriculture
Farming, fishing, etc. must be preserved. But the methods will change. There won't be any factory-made, mass-produced foods. There won't be any huge farm equipment. So farming will revert to a far simpler basis. Oxen or horses will be the main farm machinery rather than giant combines and tractors. Fishing will revert, too, to small-scale. But this is a vital industry, so agriculture won't go away.
Weapons and Self-Defense
The era of tanks and battleships and drones is done. No way your new world can support the industries necessary to build, maintain, and fuel those machines. The chemistry behind gunpowder will be preserved if the raw ingredients are available. If not, that may be lost as well. You might see a resurgence of medieval or early technology levels. Long bows, maybe swords, definitely spears.
If your survivors have access to stone, then castles may return as a means of self-defense. Especially if they come under organized attack. Even if not, they may maintain stone walls as a defense against animals. Or earthen walls as a protection from attack and floods.
Manufacturing
The days of industry and mass production are gone, at least for a while. If anyone knows even the basics of blacksmithing, those skills will become vital. If not, then people will have to re-learn those skills and fast. There's simply no other effective means to maintain metal tools.
For a generation, perhaps two, after the fall, your people can continue to use found items. But after that, they're on their own and must construct new things. Blacksmithing, weaving, dyeing, sewing. These manual skills must be learned anew by your survivors.
High Technology
You can forget technology. Do you know how to produce a radio from raw materials? A calculator? While found items can be maintained for a time, eventually electronics stop working. Or power sources run out or fail. Within a hundred years, no one will use electronics for their original purpose.
Building new electronics is unlikely, since doing so requires factories and a wide range of specialized skills. Skills that are hard to come by, rarely all found in the same area, and need too much of the resources available to a subsistence-level region trying to not die. Radios will be awesome, but they won't last a century.
If anyone can find really old, pre-integrated circuit, radios, they might can figure out how to manufacture those. But that's unlikely at best. But modern electronics require too much supporting tech for it to have survived the fall and the struggle to not die during all that.
Motorized transport
Like High-Tech, this isn't going to survive long. Searching this site will show various questions about fuel reserves' shelf life. Eventually, the gasoline runs out. Do your survivors have access to working oil wells? To working refineries? Do the survivors have the skills to run those sites? The skills and raw materials needed to replace all of the various plumbing, pumps, and other equipment required to maintain the wells and refineries as those parts fail?
If not, you've got at most 5-10 years of vehicle life for diesel engines, less for gasoline. If so, then your cars and machines may last a generation before parts become too rare. Because all of the parts inside the typical car or construction machine have a shelf life. The moving parts wear out. The metal parts rust. The batteries and electronics all age out eventually. And each one of those parts must be manufactured anew. And often with extremely high tolerances using raw materials that aren't usually all in one region. Materials that require mining, refining, and processing to even introduce to your manufacturing process.
Electricity
Maintaining electricity isn't that hard, relative to everything else above. But your people, if they are smart, will recognize that it's no longer a commodity. It's a rare resource to be used for special purposes. Your hospital needs it, for as long as their equipment lasts. If you can maintain any kind of quasi-factories or food storage / prep centers, they may need it.
But within a decade or two, they'll be using windmills. So power won't be a thing that's always on for everyone. It's just too resource-intensive to keep the lights on. And, over time, the things that need that power will be harder and harder to find.
And so within a few generations, the need for electricity will be gone. There just won't be enough things left that require it to justify the resources it takes to maintain.
A real world example
Smithsonian Magazine, March 2018 edition, describes a situation that can be used to show some of this. A documentary film maker went to Papua New Guinea decades ago and filmed a couple of documentaries. In them, a local tribe is discovered. They are shown, for the first time, ideas like "business". One of the tribes sets up a coffee plantation. They use the funds to build a fancy modern house. They get electricity and set up a satellite receiver to watch TV.
But then a drought sets in. The crops begin to fail. The film maker comes back twenty or so years later. The house has no windows or electricity. The satellite dish is rusting and of no use. The tribe has reverted to their ancestral lifestyle of growing subsistence farm vegetables and living life their way. Technology wasn't helping them survive, so they dropped it and moved on with their lives.
In times of crisis, we drop the things that don't help us survive the crisis.
Thousands of years later
After thousands of years, they may have built up enough to recover from the dark times. But those times will be shrouded in mystery and folklore.
Some tech will have been resurrected. But probably nowhere near a return to pre-collapse levels.
Think about it like this:
The Romans had roads and indoor plumbing a thousand years ago. My mother grew up on a farm that did not have indoor plumbing when she was born less than 100 years ago. And that farm was on an unpaved road. She can distinctly remember getting indoor plumbing as a child.
It takes a very long time to recover that which is lost to Dark Ages.
