Hello, mrovot!
iPhone 12 mini, IOS version is the latest possible 1.18.2, every live photo that I find from the most different sources is not suitable for installing live wallpaper. I don't quite understand what the reason is, I'm trying to use a photo taken with a camera - failure, I'm trying to use a photo downloaded from tik tok - failure. Has anyone encountered a similar problem and has a solution been found?
I had the same “problem” on my iPhone 14, until I realized that it isn’t a problem at all. Craig Federighi said in WWDC23:
And when you select a Live Photo, we use an advanced machine learning model to synthesize additional frames to create a gorgeous, smooth, slow-motion effect…
So, basically, they use AI to make more frames (otherwise it would be too short, I guess), but not all Live Photos can have that AI model used on it. For example, I’ve noticed that one can have a Live Photo of a fire burning, but not one with a person in it. It also only seems to work for photos that have something other then the camera needs to remain relatively still inside of the photo.

If you want to see this changed in the future, submit a feature request on the iPhone feedback page.
If you meant that no Live Photos can be added at all, try selecting “All” then searching “Live Photos.”

The ones that appear in the “Live Photos” section sometimes don’t appear right away because the system is trying to suggest ones that can be used. If you still can’t add any Live Photos at all, submit a bug report on the iPhone feedback page.
I hope this helps!