The ETRS(i) can operate with silver oxide or alkaline or lithium batteries...it is the only Bronica to be compatible with all three battery chemistries; the owner's manual does not mention lithium, only because the manual was never updated after lithium batteries came into existence, but Tamron (who had purchased Bronica before the line was discontinued) published information about battery chemistry suitability for the ETR, SQ, and GS lines.
The ETRS(i) should also operate with NO BATTERY at all...it would fire its shutter at a mechanically fixed 1/500.
Something else is going on with your outfit, as the battery should have no direct impact on its operation apart from fixed shutter speed at 1/500 (regardless of speed selected on the control dial), as other shutter speeds are electronically regulated.
I just pulled out my own ETRSi, no film, no battery, and confirmed that it would fire its shutter at 1/500 (by removing the film back and holding the camera lens aimed at a lit white surface while peering thru the camera from the back.)