Hoag, Thanks for your reply. I too have the 100-400 GM lens. Amazing lens! Have you had any experience with a TG-5 or the RX100? I'm interested if there is a considerable difference in image quality when you step up from a compact like the TG-5 to a crop sensor and is it worth the cost.
The short answer is no I haven't shot either the TG-5 (orTG-6) or any of the RX100 series of cameras so I am not qualified to talk specifics of one vs the other.
In general though (and of course there are exceptions) the bigger the sensor the better dynamic range and image quality you will have. Using this logic, the RX100 would likely give you better images than the TG-5. IIRC, the RX100 also gives you the ability to shoot fully manual which I believe the TG-5 can not do. this may not be something that you will be doing right away, but someday you might advance to the point where you like the flexibility that it gives you.
As you indicated, the RX100 cameras are very small and you are still dealing with a very small sensor. The small physical size has the advantages which you mentioned, plus you will be pushing a small package through the water column so that will have its own benefits. This is the reason why I suggested the Olympus E-PL9/Epl-10 package from Backscatter. A Micro 4/3 (M4/3) camera is not much bigger in physical size than the RX100 series, but it gives you the option of shooting with interchangeable lenses and a sensor that is significantly bigger than the 1inch sensor on the RX100 series. When I was using my M4/3 camera, I was able to fit my camera, a couple lenses, 2 ports & a pair of strobes into my carry-on quite comfortably. (I typically used the Panasonic 8mm fisheye, the Olympus 60mm Macro or the Panasonic 20mm "Pancake" lens.) This brings me to another advantage of the M4/3 system. In addition to the usual offerings from third party lens manufacturers, both Olympus and Panasonic have adopted this as their standard so you can use lenses from either as "native" lenses. With a M4/3 camera and the Panasonic 8mm fisheye lens, I only needed a 4inch dome port, so it was very compact in the water.
The next step up would be to the A6xxx series with an APS-C sensor. There is a step up in sensor size with the associated benefits. The jump up in physical size, however is not as much as you would think. As I mentioned in an earlier post, my current underwater camera is an A6000 in a Nauticam housing. I am still able to get my camera with 2 lenses, the housing and a port plus a pair of strobes into my carry-on. It is a relatively small package to push through the water, but noticeably bigger than a M4/3 housing especially when you start to put a wide angle lens on it. The dome port for the 10-18mm lens is a 7 inch dome compared to a 4inch dome on a M4/3. (Keep in mind that if you opt for the Sony/Zeiss 16-70mm f/4 lens, it will use the same Nauticam dome port (36129) as the 10-18mm wide angle lens so you would only need one port.) When thinking of a carry around camera, I think you would be surprised with the size of the A6xxx series. They are actually very small and make a great camera to carry around with you when you are not diving.
I think you are wise to not even consider your A7R3 as an option. Yes, it would (with practice) give you the capability of capturing some incredible images, but think of the loss if the housing floods. As the saying goes, the juice has to be worth the squeeze.
If I were in your shoes, here is what I would do, and keep in mind, this is only my opinion, so take it with a grain of salt. I personally would eliminate both the A7R3 and the RX100VII from consideration. That would leave me with a M4/3 or an APS-C sized sensor camera. I think that is the "sweet spot" in terms of future proofing, flexibility (both have interchangeable lenses) and image quality. You have already decided that if you go APS-C that you plan on a Sony A6xxx camera. Try to establish what your priorities are (size of the camera? size of the camera & housing? price? commonality with your A7R3? Image Quality? ease of use?). All of those (and likely more considerations) will factor into your final decision.
I would spend some time reading (and watching) the reviews of cameras & housings on the Backscatter website (because you are, after all buying a system, both the camera and the housing have to meet your needs.) Find out what their recommendations are and try to determine if their recommendations make sense to you and meet
your needs. If you are still undecided, call either Backscatter or Mozaik and speak with someone. Both of these companies have outstanding customer service and I would not hesitate to recommend either of them. (If you do call Backscatter, I would recommend that you speak with them about that Olympus E-PL9/E-PL-10 package I gave you the link to. That looks like it might give you a huge Bang for the Buck if you are willing to get outside of the Sonyverse.)
Like I said, this is just my opinion. No more and no less. Take it for what it is, ultimately you will have to get what is right for you.