To change the ownership of the files, you should only have to run sudo chown -R user:group directory. -R makes chown run recursively, so it will modify the directory and all subdirectories and files. Do note that changing the ownership to plex:plex or something similar would leave your user unable to normally modify the files. My solution to this was to add both my regular user and the plex (in my case jellyfin) user to the same group. That way both users can easily see and modify the files, as long as the group has read/write permissions (the 2nd column of rwx in ls -Al). If necessary, you can add group permissions with sudo chmod -R g+rw directory.
On a side note: have you considered using jellyfin? It’s a completely free alternative to plex, which recently received a truly massive update with tons of new features. Some people prefer plex’ overall experience, but I’ve been running jellyfin with almost no complaints.
Small disclaimer: I’m writing from mobile, so the commands might not be 100% correct. Run at your own risk, and NEVER POINT A CHMOD/CHOWN COMMAND AT SYSTEM DIRECTORIES LIKE / OR /USR. That’s one of the easiest ways to completely break your system.