Total noob with this stuff myself, I have been reading around,
Some applications given access like admin(?) , will have been allowed to install in critical locations to do the special tricks they do.
To fully remove these applications the special permission change made has to be disabled by the program first, then the program itself can be uninstalled.
If the program was allowed (the special permission) to make changes to critical section, then removed without the permission, it is possible for critical changes to be left. (source: fails done by commenters in google play store)
Anytime these high permissions are allowed, and these changes made, it should be turned back off first in the program, prior to uninstalling the program, or unexpected things could occur.
It is possible that a cool trick software has been installed, and forgotten, or not un-installed properly. Maybe an app that turns the screen on or off based on sencors or cameras , or phone or messages, like the proximity, or a shake , docking ? That the application has made changes, or even changes to more critical areas. Lock screen app, lock screen customiser, launcher , special trick home changes, there are hundreds of less documented tricks.
There are "safe Mode" ways of getting into the phones which keeps 3rd party items from operating, the https://android.stackexchange.com/search?q=safe+mode Android site has lots of information on it.
The search of https://android.stackexchange.com/search?q=boot+loop Bootloop. We know you do not have a boot loop, but you still cant do much when this happens, so some of the boot loop information could be applied, which is this safe mode.
Different phones use slightly different methods for getting into the safemode, adding to the fun, finding an expert with the same phone might be a thing to do if you wanted to access safe mode.