The smartphone is a OnePlus Nord CE 5G, model EB2103.
Basically, when I focus a field where I'm supposed to enter a password, a system "Display over other apps" like this

takes over and overlays the original app, not allowing me to enter the password in any way.
This happened after I upgraded to Android 12.
Here I've filmed what happens.
Any clue how I can solve this?
I've also noticed one more detail. If the app has the little eye icon to make it show the password (unlike the app in the video), I can click on that icon before focusing the password field, then when I focus it and type the passord, the annoying thing doesn't happen.
Here is the video of this behavior, but be aware that the screen never gets full black for me; I always see what's going on while I type the password.