The chins are a little sloppy. The best improvements I’ve ever made to form were when I added more frequent practice chin up sessions throughout the wee, whether it was just practice sessions or a specific progression.
One specific progression I followed is the Russian Fighter Pullup program; it was on an external site so I can’t link it.
If you don’t want to do that, just add a few submaximal chinup sets on multiple days throughout the week. Don’t think of them as workouts or even push yourself too hard on them, just practice the reps, focus on tempo and ROM, etc.
Also if chins ever bother your shoulder, you might look into finding ways to do them with a parallel grip. You could probably get gymnastics rings that could strap onto your pullup bar and set them at whatever width and angle is most comfortable.
The lockout on your press looks good. It looks like you’re leaning backwards a little bit but its hard to tell. So, if you are leaning back too much, you might need to get stronger at initiating the press. In the long run leaning back can put a lot of stress on the lumbar, especially when you get stronger. OHP is actually the only lift that has ever caused me back pain, because of my own failing in this regard