So, to me he looks miles better in that last video, with you riding. He’s swingy, relaxed, collected, got impulsion.
In the previous videos, he was mincing along without strong impulsion, as others noted. He also seemed like he was unable to relax through his poll and neck and thus looked stiff and in a false frame.
You’re paying good attention to his feet etc. Osphos did zero for my KS mare. She did find good relief with shockwave therapy, though we no longer have access to this.
Yours may be feeling better in his back, but the way his muscles looked in the trainer videos made me think he’s sore kinda all over. If he were mine, I would spend a solid month walking, walking, walking on a loose rein and then I’d walk some more. I’d do Posture Prep, Masterson Method or Equine Body Work Online with him as often as possible. (That equinebodyworkonline dot com is cool - she’s got these audio guides for different parts of the body so she’s telling you what to do as you’re doing it. My horse loved it. Some of the info is free, but I think you can pay by the month or for a full year.)
After a month of this, I would video again and assess. I’ve seen more than one horse recover well from walking as a foundation for fitness, suppling and all over muscle soreness. Plus, there’s something about the simplicity of walking that takes the pressure off horse and human, good for both partners.