Not 100% sure but I think so.
The connection to a cellular network (as well as receiving/initiating a call) will need more power for a short period of time (Leistungsspitze / power peak). And I guess your battery is quite old?
I had this iirc with a battery that else worked fine, still long enough but let the phone shut down in such scenario.
Please try the same with a connected charger...

--edit
ah, I did not see your other answers. So self tested already.
Your battery is worn out and cannot give enough power juice for such peaks anymore.