Question about Samsung T7 Shield

Yes, that works - I did it that way too. Just use the usb-c to usb-c (from ssd to mobile) cable and it works :)

I don't know the connection and transfer capabilities of a Samsung Galaxy S22.
If you can transfer your photos from the phone to the computer, then the answer is yes.
If your question is whether you can connect the hard drive directly to the phone to transfer photos, unfortunately I don't have the answer.
Have a nice evening

if you have a USB On the Go adapter, yes.