With a clean install of the OBS-Studio Snap, and with the Videos directory relocated to a directory under /media using the ~/.config/user-dirs.dirs file with:
on starting OBS-Studio with Videos directory is deleted and replaced with a self referencing symlink:
Videos -> /home/paul/../../../../../media/paul/data1/home/paul/Videos
Manually editing the Recording path fixes this, even if the path is still under /media, so long as it is not a directory referenced in ~/.config/user-dirs.dirs (tested with the Music directory).
I have tested this with content in the Videos (and Music) directories, and thankfully the directory is left in tact and not deleted.
My original plan was to use bind-mounts to relocate the directories, but this breaks the Rubbish Bin feature of Nautilus, so for now I am using this method.
Permissions have been modified as per the documentation for the OBS-Studio Snap.