Maybe in some niches, but for most modern ILCs (e.x. Sony E mount, Nikon Z mount, etc etc etc) it is typically some form or another of On-sensor Phase Detection coupled with Contrast Detection for finer tuning.

The biggest advantage compared to older SLR designs are that Phase Detection can now work with full light (vs whatever got split off on an SLR pentaprism for the dedicated AF sensor) and can work in conjunction with the contrast Detection for fine tuning focus.

Then, of course, all the predictive stuff added in the last 10ish years as far as processing sensor output to detect eyes/birds/motion/etc.

No. Modern cameras usually use a combination of contrast detection (pure image analysis checking the contrast of the region you want in focus), phase detection (an optical system where you split the income image in two and then compare them) and sometimes help of some sort of assist lamp.

https://en.wikipedia.org/wiki/Autofocus

The only AF systems that use LIDAR are the one on the newest Hasselblad medium format mirrorless cameras (since DJI owns Hasselblad and can leverage the tech from drones/cinema cameras) and possibly some phones.

I suspect it's fairly challenging to implement since the LIDAR sensor doesn't operate through the lens, so you'd have to continuously align the depth map with the image to account for parallax; plus it's only useful for close-ish distances (since the lasers can't be too powerful) and can cause unwanted focus behavior with windows or reflections.

I think only in certain cinema rigs. See DJI's products eg https://store.dji.com/product/dji-focus-pro-lidar