But the way we squat bodyweight is not the way we squat with a load. Not to say a really heavy load.
Several things:
1) It doesn't need to be the same, it needs to have the same attractor states. You establish these with BW and build on them.
2) If you can't knock out a bunch of bodyweight squats with no issues (mobility, strength, endurance etc.) then you have no business loading it heavy. You're just going to strengthen a faulty pattern bc you're starting from an unbalanced base ("shallow attractor wells").
3) Once you can load the squat, you should find zero difficulty mimicking this pattern with bodyweight. So you can do bodyweight squats the same way you do heavy squats. This is entire concept of warming up - your form with the bar should be near identical to your form with 100kg. Take the bar away and it should be the same, just pretend there's a bar there (elbows back, tight back, etc.)
We do have favorable leverages etc. but I think they're best learned by doing lots of training on different (barbell) squats and after years, finding out what's really best for you. Something may be easier to recover from, something better for muscle building, something better for your powerlifting total, etc. No reason to paint everything with a single brush.
I'm not painting anything with a single brush. I'm arguing for a proper starting point that allows for a natural progression to other variations.*
With squatting, this is bodyweight. It might even be a regression from bodyweight (e.g. rocking).
I originally phrased it as "finding your natural squat pattern" as I didn't think "re-establish your attractor states" or "re-establish joint centration" was quite as catchy.
*From what I saw in the video, the OP doesn't have a solid base to build on. I doubt he could mimick that LBSQ technique & depth with just his bodyweight.
Which means he is using the weight of the bar to overcome tension AND create tension. This is how injuries happen.