No camera will, in and of itself, double as a dive light. On the contrary, with exception of very close range macro shots, you will usually need additional lights (constant LEDs or strobes - both have their pros and cons) to produce good-looking images or video.
Olympus TG-5 and SeaLife DC2000 are the two best 'waterproof' cameras currently on the market. Both can be dived to 15-18 meters bare, but require a housing to go deeper. Note that while they're marketed as waterproof, they rely on very thin and fragile o-rings to maintain sealing, and can flood as easily - some say more so - as any housing if not maintained properly. If you put them in a housing, the waterproofing provides an additional safety margin - even if your housing floods, the waterproof camera inside will almost certainly survive the ordeal, whereas a normal camera will be dead as a doornail.
TG-5 has a zoom lens and a very useful macro mode (focuses as close as 1cm from the lens), but has a smaller sensor and lacks shutter speed controls. DC2000 has a larger sensor (same as Sony RX100 III) which can produce higher quality photos, and a full set of controls, but its lens is fixed focal length and can't focus as close. Additionally, if you shoot it in RAW mode (as you should, underwater) it takes several seconds to cycle between shots.
GoPros and their clones are okay for video, but forget using them for stills. However, their small size brings some unique advantages - a big camera ring, with a handled tray, arms, lights, strobes, wet lenses, etc., pretty much dominates your dive. At no point during your dive can you forget that you're towing it, and most of your dive time will be spent looking for photo/video opportunities. An action camera, on the other hand, can be hung from your wrist, or stuffed into a BCD pocket, and only brought into play when you want to take a short clip of something interesting. You can also put one on a stick and bring it closer to a tricky subject than you could with a large camera rig.
If you have a phone with a good camera, you can put it in a housing and take it underwater. Weefine Smart Housing (Kraken in North America) pairs with an app on your phone via Bluetooth and controls the phone wirelessly via buttons on the housing. It also has a pressure sensor which allows the phone+housing package to double as a dive computer.
On the upper end of the scale, you have the premium compacts - Sony RX100 series, Canon G7 X series, Panasonic LX10/LX100, etc. Each has its own strengths and weaknesses, but they all require a significant investment in both money (housing, tray, arms, lights, strobes, wet lenses, batteries, chargers, cards, software, etc) and time (learning how to use it all) to extract good images out of all that hardware.
