Inability to change permissions on iMac running Big Sur

Just installed Big Sur and Time Machine backup on an external SSD drive connected to my mid 2015 iMac via USB 3. Everything seems to be working except that I am having issues with the "you can only read" message when I "get info" on my hard drives. I can physically still save files on my computer's desktop or document folders, but I can't open Dropbox, or run BlackMagic drive speed test, etc. I get the "You do not have permissions to ..." I am aware that Apple has some built in protections to prevent people from doing damage to their systems, but I do not believe that I am getting near that "line" in simply trying to open Dropbox or running a speed test on my drives. Any help would be appreciated greatly.