I’ll keep this simple and try to save you money, cause I’ve seen this lots and fixed it lots.
Firstly, hamstring function messing up the back and squat form is completely overrated and mechanically makes very little sense at all.
Second, practice your squat doing the following unweighted.
-start to squat, and you should be able to feel where something at your hips wants to pull your back around, probably the part where you’ll feel your back going. What you want to do (unweighted squat) is use your hands and push down into the front part of your hip, into the bit where things are folding over. This will be the muscle in front of your hip joint. You want to give bit of a push in, and imagine using that push to trigger the muscle contraction you want to help move you lower in your squat. It sounds crazy, but for alot of people you get a good squat depth by driving into the depth from the front of your hip (like something pinching and pushing from the front to help drive you down on the angle you want).
This may feel awkward the first time, but you may find yourself at a good depth comfortably.
IF this all happens and I’m actually right, you definitely need hip flexor stretching work. For this, stand with one leg in front of the other. Lean back, then lean to the opposite side of the leg out behind you. This will stretch in those deep hip flexor muscles that are likely causing the issue.
Other muscles tend to show up as other problems in the squat, but this will be a starting point. Till you can do unweighted squats to depth with good form (practicing the push from the front till you can initiate it on your own), don’t bother with loaded squats.
A nice trick to practice (unweighted) is on the descent, when you are getting near your sticky hip point, lift your toes a little bit to help get weight distribution right.
Those videos above show absolutely nothing regarding back form or any issues there, although HIP positioning and overall technique was different. The reality is that top Olympic lifters MUST maintain a relatively neutral lumbar spine or they get injured. Nitpicking anything about those technique videos is nonsense.
That is all.