Bluetooth speaker not listed in Output despite being connected

MacBook Air M1, Ventura 13.3.1

My JBL Bluetooth speaker is paired and connected with my MBA but the sound is played only by the MBA itself, not the JBL. The JBL speaker is not even listed in the Output section in the sound settings - only the MBA speakers. I have followed several tips including some commands in the Terminal as well as rebooting and re-pairing the devices but nothing works which is utterly frustrating since my MBA is not even a month old.

Can anybody help me out?