I think we're all agreed that it not severe damage. I don't think you can classify it as a flameout either, as something else has gone wrong given the engine indications.
So you neitber need to jump onto an extended recall that has you closing start levers and messing with engine fire switches. Niether do you want to wait until clean and stable before doing anything. Hence the engine limit, surge or stall checklist. Minimal recall to reduce thrust until indications remain within limits or the thrust lever has closed, then shut down the engine at your lesuire later.
Making the appropriate choice is all about understanding the precise wording of the condition statements and the objective (if stated). This is something not fully appreciated by some pilots, they only memorise the actions and thus occasionally fail to correctly select the most appropriate checklist.
It would be entirely innappropriate to start jumping to conclusions about shaft failure or whatever. Such troubleshooting is only appropriate if you have multiple failures crossing checklists or there isn't an appropriate unanunciated checklist available.