I think that you ( simply ) have a sleeve that has flutes and the barrel section snapped off from wear and “work hardening”…where metal just can’t hold temper any longer, along with dried up lubrication .
You will have to research the model using the serial number on the watch movement..but also cross referencing the case manufacture for that size of watch,..as one didn’t correlate to the other in many cases.
You may even find that you will have to send the watch and case to someone for a “fit”.
This can be a bit of a daunting task at times.
I would try Dave’s watch parts for starters..then Otto Frei if he can’t help