A few thoughts on the 360 cameras and what I have learned. The Vuze you posted looks like it will be the best available consumer level camera available for our purposes.
Underwater 360 needs to be recorded in 5.7k for really good quality. 4K stretched out over 360 degrees just doesn’t produce sharp images underwater.
5.7k cameras run really hot in 5.7k mode and will automatically shut down if they get too hot. It helps to turn off WiFi in the camera and any other options that are not necessary. Put the camera in a tight case and it will build too much heat pretty quickly. It will be interesting to see the Vuze solution. I think this is why we don’t see any good options on the market now. Bluerobotics tried putting a small fan in a housing but I think they have abandoned the project.
5.7k videos are massive and take a long time to process, upload, and are not very easy to share. Just something to keep in mind and should improve as the tech does. The popular video hosting sites don’t support 360 5.7k yet.
Lights, if you have a 360 view you are going to want 360 lighting.
With all that in mind I think it can be done with the right enclosure and light attachment. The enclosure I put together works in 5.7k with my Garmin 360 Virb and a LED light. It’s big but holds a light, camera and a lot of air which makes it close to neutrally buoyant. The aluminum end cap probably helps with heat dissipation in the water. A more streamline enclosure could be done, I think, with two clear dome end caps attached to a narrrow aluminum body. The aluminum body could have fins on the outside like a radiator and a vent so you can close it up after warming it up. You will want an extension to get it away from the ROV which could also be aluminum, hollow, and act as a heat sink away from the camera.
That would also lower the center of buoyancy which may help the Trident dive with just the vertical thruster.
My plan with the Trident is to sandwich some floatation between the bottom of the Trident and some 1/4” HDPE via the mounting screws. Then, attach the housing I made to that. I tried hanging the enclosure directly from the Trident but it needs buoyancy at the corners to keep it stable.
Best viewed with the app or on the website. https://youtu.be/13RIcce2AyQ