Super glue is actually a good glue to use for this repair.
BUT... ONLY after the binding has been made to fit back into the groove. If you just flood it with CA (Super glue), you will make a mess and a half for someone to deal with.
This is not a structural problem. You should do nothing until you're ready with a couple hundred bucks or more to bring it to someone who knows how to fix this. Then, ask them what they want to do, and let them do it.
It does not need to be stabilized. It's already moved. It won't change the tone or let moisture in (it's already in, just physics).
It will get, marginally, more difficult to repair the longer you let it sit. But probably not enough to really impact the cost of the repair, unless you do something unnecessary like fill it with polish residue or something.
I did a similar repair recently:
(I used super glue. But there was more to it than that :-)
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