I got into SUP because of bad rotator cuffs.... I couln't pop up on mu surfboards any more.
SUP has been fine with my shoulders.
I make sure not to macho out and race, or train hard.... but I spent 20 hours on boards last week.
I can't even tuck my pants in, or touch my hands behind my back.... but I can SUP all day
I hope you have a speedy recovery.... just remember not to push past a point.
I can paddle hard for waves.... but I paddle smart the rest of the time.
You might want to ride a board with a bit of easy glide, until you are stronger.