I personally would not run my mount as root as I always run it as a non privileged user.
If he/she can touch the file as the proper user which Radarr is running as, Radarr should write its test file:
-rw-rw-r-- 1 felix felix 130 Mar 28 07:04 radarr_write_test.txt
That’s the only thing Sonarr/Radarr tries to do.