I'm an above water Sony photographer noodling this same question.
The main improvement of the rx100-v over the rx100-iv is the autofocus system. If you want the camera to shoot action above the water, as well, that advancement could help, but for underwater use, I'm not sure you'll get much benefit from the latest model. You can still buy an rx100-iv or even an Rx100-iii brand new for less money. The IV got a sensor upgrade over the iii, but I haven't investigated how substantial it was. Sony offers a single housing that works for all generations of Rx100 models. Just an FYI - I haven't used or even inspected one.
The Rx100 gives you an all in one solution for a lot less money total, but it's not expandable, and you won't get results as good as you can with the A6300. A larger sensor can capture images with a lot less noise in the lower light frequently encountered underwater. The sensor on the A6300 is almost twice as large. Or,just look at the diameter of the front lens elements, and it will be obvious which let's in more light. The total cost is going to be a lot higher with an A6300, though, and you'll need different components to make different lenses work in the various housings. Each of these ports and gears costs a fair amount of money. There are cheap housings, but if you're going to take a more expensive kit underwater, you can easily justify a more expensive housing to protect it. The Fantasea seems like a decent budget option.
To go with the A6300, you need to figure out which lenses you want to use and then find a housing with ports available for the lenses you want to use. Make sure the Fantasea actually has your desired lenses covered.
I'm a minor fan of Zeiss and own a lot of Zeiss glass, but even so I wouldn't get too hung up about the Zeiss badge. There are Zeiss lenses, there are Sony lenses with Zeiss' T* coatings, and there are Sony lenses which Sony claims to have some participation by Zeiss in the design process (so called "Zony"). Zeiss' own lenses tend to be good, for a price; worth it to some people. But, the Rx100 isn't a Zeiss lens. Rather, it got their T* coating, and I doubt they have any other involvement. The T* coating is good. It bumps color contrast. But, I doubt you'll see much difference underwater, really, given the lighting down there. There are true Zeiss lenses for the A6300 (the Touit line), and they are relatively good, but neither Sony nor Zeiss put their best efforts into APS-C lenses. I'd just consider the Zeiss nameplate little more than marketing for the purpose of this discussion, frankly. You'll get the best images by putting Sony's full frame glass on the A6300. Those lenses also tend to cost more and there may be issues getting the housing to accommodate them; dunno.
My $0.02...