I have done some research using data from imaging resource quite interesting
Autofocus Systems for Underwater Photography
Autofocus Systems for Underwater Photography
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I don't think that article really gives the best analysis of the situation. But, maybe my experience is too limited.
In my experience, the speed of autofocus underwater is not nearly as critical as it is for shooting BIF (birds in flight). The subjects I have shot do not move nearly as fast as BIF, generally, and they don't usually appear with so little warning as you get with BIF.
The vast majority of the time, I have my focus locked onto my subject well before I actually release the shutter. And, yes, I am talking WA, as that is almost exclusively what I have been shooting.
I do agree that accuracy of focus is critical. To me, that is THE MOST important characteristic of the AF system for shooting underwater. Personally, I am just not able to manage manual focus when shooting moving subjects underwater, so I need it to be pinpoint accurate.
Also, the chart is no longer current. One of the reported improvements from the Sony a7rIII to the a7rIV is speed of AutoFocus. I have shot some BIF with my a7rIV. Some shots have been where a bird suddenly dived into the water after a fish. For those shots, I whip my camera up and shoot as it dives. The whole scene is done in less than a second. I have gotten 2 - 4 frames in that time, all in focus. So, I don't think a metric of >0.25 seconds is close to accurate for an a7rIV. But, I could be wrong, as I don't know what the test conditions were for the numbers in that chart. And, of course, what I've said is purely anecdotal.
My other anecdote on the subject is letting a friend play with my camera who shoots semi-professionally using some top shelf Canon (I can't remember which model). After a minute or two of shooting his dog running around the yard, his first comment was an emphatic, "man! This thing focuses FAST!"
Another thing that does not seem to match my experience is that you've reported that the Sony does will at focusing in low light. With mine, that is one of my biggest complaints. Without a focus light, it really seems to struggle on focusing on things underwater that look to me like they are easily lit well enough to get a focus on. But, I am talking about an rIV and you are talking about an rIII, of which I have no direct experience. So maybe that is a difference between them.
There is another reason that I don't think your article gives the best analysis of the situation - a reason it does not really demystify in a way that has practical application.
AF speed is very dependent on the lens used. It is well known (in some circles, anyway) that the Sony 90mm macro lens is the best macro lens available for a Sony camera. But, it is also very slow to AF. In contrast, other lenses on a Sony achieve focus very quickly.
The article does not acknowledge this fact at all, much less caution the reader to take this into account when choosing a system. The chart that gives numbers does not say what lenses were used. Overall, it is completely misleading because the numbers could be completely different if the cameras were tested with a different set of lenses, leading to a totally different conclusion.
By not even mentioning that, it would mislead the less-knowledgeable into potentially buying into a platform that "makes sense" based on the information presented, but in reality could be the absolute worst choice for what that person wants to do.
Sorry but now you are being picky at least there is some foundation and explanation how to read information compared to the crap that is already been written everywhere including review posted by people that sell the equipment
I always get responses from those guys whose system came worse than what they expected and then there is a start of if and buts to build an argument that what I wrote is flawed, you hear nothing from those whose camera appears to do well, wonder why
For what concerns Sony cameras they are quite popular among new comers but extremely rare within pro and people that win competitions so for what matters the marketing did not convince those guys yet. Has this got a link with what I wrote am not sure but those are the facts
If you are happy with your camera just go and get some images to proof the point that is a great camera