The Panasonic Lumix LX10 is arguably the best compact, point and shoot camera for underwater video on the market. It uses a whopping 20MP sensor and shoots beautiful 4K video that you could expect from a high-end mirrorless camera. The footage is sharp and detailed due to the high megapixel count for such a compact camera. The f-stop ranges offered by the built in 24-72mm (35mm equivalent) lens allow for beautiful bokeh as well.
The GH5s is popular for underwater video because the camera is at a great price point, the body is relatively small, there is a multitude of micro-four thirds lenses available for any lens requirements, the video bitrate is quite high, and camera supports many video features that other micro-four thirds cameras do not support. It crushes all other micro-four thirds cameras at high ISOs with respect to noise.
There have been many improvements in the compact camera lines over the past few years. Larger sensors, faster focusing, and more controls have all led to a selection of cameras that work smoothly, keep size tiny and are functional with a variety of lenses and accessories to round out your underwater photography experience. Sony and Canon have both given their compact cameras one inch sensors, and greatly improved focus speeds over the cameras of a few years ago. Olympus continued to add features to their cameras while keeping both price and size down.
Then there's resolution and video quality. You'll want a camera that can record in 4K for sure. The top-end models from DJI and GoPro offer 60fps 4K with digital stabilization that's absolutely incredible. They're also not limited to ultra-wide views; you can set a narrower angle to remove lens distortion, making them solid choices for vlogging and travel logs.