I can't have the regular YTM. In app manager, it says it's not installed for this user. Installing from the play store doesn't work.
Not installed for this user - but is it installed on the system?
Ie, if you had eg YT pre-installed by your ROM as a system app and by pm command(s) you disabled or uninstalled for this user - but it is still installed on the system, then it doesn't matter if it is not installed for this user - it is still installed on the system. And when you try to install YT RV root version, Android recognizes that another version of the same app (same package name) is already installed and doesn't allow to downgrade, corresponding to the system pre-installed YT app
Use YT RV non-root or if using root version make sure that YT RV you are installing is newer version than the pre-installed one, or first properly debloat (not by pm commands) the pre-installed YT version if it is newer than than the YT RV
Since YT RV Ext is on hold for some time, might be that you have a problem here - YT RV Ext root version is like two months old. You can try YT RV not Ext, it should correspond to the newer YT app version (I don't use not Ext, don't know its version number)
Eg, my YT RV Ext is 18.17.43 but the latest YT official is 18.22.36 or so.
You cannot have pre-installed com.google.android.youtube (same package name) v18.22, and then to install v18.17 just for your user (no matter if it is user 0 or user 999)
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Edit:
If you are talking about YT Music - latest official is v6.05 51 or so, latest YT Music RV Ext (root) is v6.01.51, but it's the same package name com.google android.apps.youtube.music and again, downgrading corresponding to the newer system version would not work no matter 'if for a different user'