I think I could simply try to glue it, but it may be better to replace the socket.
I’m not a DIY guy, but before trying to find a place that could repair it, how difficult it could be to replace it?
It’s a very easy repair, just a matter of desoldering the old jack and soldering a new one (the whole jack is damaged, you won’t be able to put back or glue back the part that broke).