You should know that I posted this here to make you laugh:
https://hackaday.io/project/186310-crane-built-from-old-fence

Well, looking at "solenoids" is just not the right call. Basically the same thing is used under the name "voice coil" which supports linear motion and is widely used for precise but short ranged motion. So many categories have more options inside them than you might think at first glance.

Ooh, I'm out right now, but will definitely look those up when I'm stationary. That's precisely the sort of thing I'm looking for!

If you are interested in small but precise motion have a look at flexures in general and https://openflexure.org/ for an open source implementation for microscopes or optical fiber alignment in particular.

I do not.

And I doubt such a list is really feasible. As you already said there are just too many properties such things have. Also most types don't have easy values but large ranges - overlapping with most other types. Then most properties influence each other. While belt drives are for relative low forces large enough belts will still transmit more force than a small lead screw. So the absolute values are not that interesting. What is interesting is what compromises you need to make to push things to the limits. These compromises are by their very nature complicated and depend a lot on your use case.

Then it sounds like you are looking for the best solution. But in engineering the better question often is what's the worse solution you still can get away with.

Even worse many choices are not driven by the best aspects of a product but by what does not have properties that prevent it being used. Something may look great on paper but some minor thing may prevent you using it anyway. May be you are dealing with a dusty environment that will get your sliding rails stuck. Or you just can't have the magnetic field of your solenoid as it messes up your measurements.

So as a novice it is often better to look at existing solutions and then try to understand their design choices. If things seem too complicated or expensive ask yourself which properties they are able to achieve by their design and why you think you can get away without them.

It makes sense that there won't/can't be a definitive list. But I don't see why there can't be a set of guidelines/rules-of-thumb. In fact, in my frustratingly-slow research, I already could write a partial one with some level of confidence. It just feels like someone with more actual industry/hands-on knowledge should have done this already.

For instance, belts have fairly high limits as long as you can use very big belts, and you don't need very sharp bending radiuses. Belts can also have some interesting geometries, allowing them to dodge obstructions, where most other forms have a soft-requirement on being point-to-point. There is backlash in a belt, but with modern belt design that can be very small to the point of often being negligible. Belts do wear over time, need tensioning (though the amount often isn't very precise) and don't need any sort of lubrication.

Solenoids only really go between two different lengths, and tend to be pretty small travel distances. For my purposes, this rules them out, so I haven't gone that far into the other tradeoffs.

Rack and pinion has backlash, you can get around that with a split pinion. Unfortunately split pinions seem to be lacking in readily-available documentation outside of one or two companies selling commercial solutions, so I don't know how trustworthy that is. These often do need lubrication, depending on your materials chosen, the ones that don't need lubrication, or don't need as much, also handle lesser loads.

I could go on, but you can see how it is possible to write some useful rules of thumb even with all you said being true.