I went to the DEMA Show for a day last week to check out underwater photo gear (and to see old friends and colleagues).
360RIZE announced underwater housings for the Samsung Gear 360 and 2 x Kodak SP360 4K, and were also showing their 6 x GoPro (Abyss) with Bullet360 sync. The Samsung and Kodak housings are expected to retail for around $1K.
The Abyss housing uses Bullet360 sync, which allows for power on/off, triggering of photo/video record, and sync assistance (for post) via an audio buzzer that goes off 3 seconds after record.
You'll see that all of these underwater solutions featured full-hemispherical dome ports, which are required to preserve field of view underwater. They also act as a negative diopter whose strength is related to the radius of the dome, which is why these domes are so big—the radius needs to be large enough to allow the lenses (often, fixed-focus) to focus underwater. Incidentally, small dome ports are why the OEM housings for the original GoPro HERO 1 and 2 didn't allow for underwater focus—the cameras simply couldn't focus close enough to be able to focus behind such a small dome port.
To increase sharpness, some folks pull focus closer on cameras that will be used only underwater (can be accomplished on GoPros by turning the lens, for example). This is the equivalent to adding a positive diopter (close-up lens) on lenses used in non-360 underwater photography, which is fairly common practice.
Some manufactures like Nikon have included accessory flat lenses for underwater use of their 360 cameras (e.g., KeyMission 360 camera). These flat ports allow for focus underwater, but have the unfortunate effect of making the camera no longer have full lens coverage. This means that the KeyMission 360, when used underwater, will no longer produce a full 360 image—there will be no overlap between the two lenses.
In the very short term, I expect the Samsung and Kodak housings to be popular; they are the only working, "affordable" underwater 360 rigs that allow for access to buttons.
The 360bubble systems will also work, but do not provide access to camera buttons.