Without knowing your specific tank parameters, it is impossible to really know more. Specific gravity can be "fine" for fish only but fatal for these stars.
I would also say that it is a very very highly stocked tank for such a young tank. Ideally, IMO, seastars should not be added until the tank is at least 6 months old, to allow several parameters to stabilize (that we don't even test for). The age of the tank is a concern for me.
This is not an easy star to keep but if it is at least more than a month old, that is good news. But this still is, IMO, a bit on the small size for this star AND another similar star. Most will not survive beyond a year and a half, and die of starvation. Two similar stars speeds up that process, IMO.
It is extremely unlike the arm was "caught."
It is possible the arm "dropped" as a form of asexual reproduction.
Only time will tell if it will improve. If the arm does not appear to heal then I would be very concerned.