Well, I see improvement from that first video you posted. Wans't that the one where the saddle slipped and you got dumped? or am I misremembering?
I see what the others see,. more or less;
you should probalby not canter much yet, you are in danger of falling off at this point because your seat is just too precarious right now at canter.
definintely take the stirrups up a notch.
At the trot, you are very braced in your leg. see how there is total air under your leg from almost mid thigh downward? even your knee is almost off the saddle. you are resisting the horse by making yourslef "strong!"
Make yourself weak. make your legs just drip down the sides of that horse. pretend you have no sensation in your legs, like you are a paraplegic. you must ride from your seat only, since your legs cannot grip.
Of course, while you are posting, your legs do work and they have feeling, but they just are soft and like springs. think of pushing softely down into the ground, PAST the stirrup, when you post, with your knee bent, ankle bent. IF you start getting a lot of air between your knee and ankle , you are bracing and coming off the horse.
once you feel a bit more secure by balance over your leg, instead of brace, you can post slower than your horse wants to go. This will make him slow down to meet you, without so much pull on the reins.
AS for canter, you must really be free with the lower part of the body and cannot brace your lower back at all.
Can you sit on a swing and swing on it , without holding onto the rope/chain part? you have to keep your upper body uprgith , while allowing your pelvis to follow and move with that swing. you ride YOUR pelvis, while it rides the hrose/swing.