I used the Sony 16-35 f4 underwater for a long time, and it worked wonderfully. I have never had the desire to shoot below f4 since the high ISO performance of the A7III is phenomenal (typically I shoot around f8).
I switched over to the Sony 12-24 f4, and it has worked quite well but it is less convenient with the Nauticam housing I am using for the A7III. With the 16-35, I could slide the entire camera in and out of the housing without disasembling it. The 12-24 is a physically larger lens, meaning that removing the A7III from the housing requires disassembling the housing and camera as well.
That said, most of my dives involve less than one hour of shooting per day, so I only need to swap out the battery every third day or so. That makes it not as big a deal for me. The shift from 16mm to 12mm was worth the inconvenience, but if you find yourself needing to do quick battery changes on deck, might not be the best choice.