I don't have an A7Riii, but I do shoot an A7iii above water. (I shoot an A6000 underwater and use it as my back up body.)
Keep in mind, since I don't shoot an A7 series camera underwater, my recommendations are based on opinion, not necessarily fact.
First, and this applies whether your shot is above the water or underwater, an image from an A7Riii will be a huge file! Make sure your computer has the "horsepower" to effectively do post production on it. If your computer can't handle the image, then you have hit a "deal breaker" right away.
As for housings, there are only 2 that I would seriously consider,
Aquatica and
Nauticam. I'm sure that there are lower cost options available, but the A7Riii is an expensive camera and with housings, you usually get what you pay for. Personally, I like the Aquatica housing for the A7iii because it offers a choice for how to trigger the strobes and will include an optical trigger at no extra charge if that is what you opt for. Both of these housings offer the capability to "vacuum seal" the housing.
For a full frame camera, your choice of lens will seem to be wider than with a crop sensor. For wide angle, the Sony/Zeiss 16-35 f4 OSS is a great lens. (It is my "go to" lens for my A7iii above water.) Both Aquatica and Nauticam have port options for it. If you want a slightly faster option, and money is no object, the Sony 16-35 f2.8 GM gives you an extra stop, but at a significantly higher price point. For macro, your best option is probably the Sony 90mm macro lens. Again, both companies offer port options for this lens as well.
To answer your question about what housing I use, I use a Nauticam housing for my A6000 with the Sony 10-18 lens for wide angle and the 16-50mm kit lens when I could get a mix of wide angle and macro.