The A7 III, with its compact and ergonomic design, has been a very popular camera for video recording. The battery life is drastically improved compared to the previous A7 Series cameras, which was a primary complaint of Sony Alpha users and is particularly beneficial for underwater video, as it allows you to shoot for much longer without the need to open the housing. The A7 III also has dual SD card slots, which play an additional role in the maximum allotted time you can record underwater without having to open the housing. The auto-focus during video works very well.
Before you start digging into the reviews, a few notes on choosing a cam that's right for you. You'll definitely want to consider frame rate, expressed as frames per second (fps). Some action cameras offer up to 240fps recording, while others only go to 30fps. For standard playback, 30fps is perfectly fine. It's when you want to slow footage down in editing to create dramatic scenes that frame rate matters. Footage captured at 240fps can be slowed down and played back smoothly at one-quarter speed. You may also want to go for a cinematic look, in which case you'll want one that has a 24fps capture option, the same speed used by most Hollywood productions.