When pilots check in with a different controller, how to reference flight level?
The word 'maintaining' is used, not 'level'. Using your example it would be:


(ATC Facility) Baron X5XS level maintaining FL 250.


The pilot can say maintaining if they're expecting higher/lower, otherwise omit maintaining altogether:


(ATC Facility) Baron X5XS FL 250.


If climbing/descending:


(ATC Facility) Baron X5XS climbing/descending FL 100.


On the first contact with a radar service, for example going from tower to departure, the SID and passing altitude are also mentioned:


(ATC Facility) Baron X5XS on the STACK 1C passing 2300 for FL 60.


In a busy environment you may be asked to 'report call sign only', in this case:


(ATC Facility) Baron X5XS


Local guidelines should also be used if different. I couldn't find examples in ICAO Annex 10 and Doc 4444, but clear examples are in the UK's Radiotelephony Manual (click image below to view).