@spoqen Looks like a standing pullover so will work front delts more. Then squat and curl. Basically no real chest stimulus.
Consider getting a Mark Bell Slingshot. Essentially gives you an external extra pair of pectoral muscles. Since they are elastic bands they will provide more assistance at the bottom of a push movement and less at the top. The bottom is where you are most likely to aggravate your shoulders and this is where you will get some support. This may help you get back to doing all typical presses again.
Other considerations:
Play with hand placement and width. Narrower may be easier on your shoulders.
Mindfulness of external rotation (elbows tucked, not flared) at the bottom of a press helps to avoid putting extra strain on shoulders.
Using rings for push-ups could give your shoulders the freedom to move in a path that suits you better. Start on your knees to make sure the instability is ok on your shoulders.
Assisted Waiter’s press may be something to try. Good upper chest stimulus and may be good on your shoulders. Elbows tucked in to minimise shoulder rotation through the press which may contribute to shoulder pain.
Hope this helps and good luck.