I experienced the same issue. A bit of web searching turned up a post that shines a light on the issue. At the time of first installation, there is an alert that appears once, and only once, regarding the need for you to jump over into System Preferences > Security & Privacy to grant a permission. If you miss doing that in the sequence, the software fails to work and the opportunity to have granted the permission is gone.
The OP of the post walks through a process for totally cleaning house on the PSSD software so as to cause it to believe that it is once again performing a first installation, and therefore prompt you again. When I tried the process, it failed to prompt me, but others in the thread reported success.
In the end, I am using my T7 as my TimeMachine. Once I knew that the PSSD software was not necessary, or even desired, for that function I just wiped the app from my system and have not looked back. Obviously a major lack of effort and clarity on Samsung's part when it comes to the PSSD app on Mac Big Sur.