Do you really want group requests going to your inbox?
Why not send group requests to a group inbox (doesn’t have to be the same one) to group/filter them that way?
One other trick with messages is that you can prepopulate the body with a template, using %0A in the URL to specify line breaks.
One of the COVID volunteer groups I work with has a request link which generates the PM to a group with preset title and body template. Has been surprisingly effective.
Because we have more than 10 groups, and each user is added accordingly. PMing me really helps, as I am managing the whole situation and tags make it even easier! Otherwise, we would need to create one more group for me, which clogs up the group section more and it’s a great way for trolls to take action.