WOW -- the randomly changing colors mid shot on the A73 III have got to be a bug. Very weird one at that. But unless there's a fix, it really renders the camera unusable underwater.
White balance on most cameras works fine down to 5m (or roughly 10000 kelvin ambient light temperature.) Most also work ok from 5-12m, though older generation Sony cameras (e.g. A7RII, A7SII) did not MWB in this range without a red filter.
Likewise, at 50m depth, ambient light is quite dim, even in clear Mediterranean conditions. So there's less ambient light for your video lights to compete against, and I imagine both auto white balance and daylight white balance would work just fine for foreground objects lit by video lights with the background being predominantly blue. If you keep the MWB in below 7500k or so, you're not going to run into purple water column issues (those arise when MWB boosts the red channel too much to try to compensate for lack of red wavelengths).
In my view, it's really the range between 12m-20m where good underwater MWB can show off. Below 20m, the colour spectrum is so skewed that even with 'accurate' MWB, things look weird. Above 12m, most modern. cameras do fine.
Indeed, the Z7 II looks "ok" at 12 meters. So no reason to think the Z9 would be worse. And to be honest, I've never felt very compelled to MWB below 12 meters, because the colors start to look unreal. They don't look any more real on Canons below 12 meters, -- but Canon's philosophy seems to be to desaturate everything, including the blue and green channels, so at least they look less obviously /wrong/.
TL;DR -- You probably don't very often MWB for ambient light below 12m. Down to 12m, Nikon, Sony, Canon, Panasonic all still seems relatively fine. So maybe we're making too much of the MWB thing.
