Try another browser? My banner on my PS disappeared a few years ago. Etsy said "Oops" and it was not recoverable. I just never replaced it. Also tr getting the PS from the order singly and then by clicking the choice box and getting the PS option up top and see if it make a difference. If you are on an app, try a browser.
I just printed a packing list with no problem, so it seems to be an isolated issue. As @hopeandjoystudios mentioned, trying another browser might solve the issue. Are Invoices having the same issues? Even if settings don't seem to have changed, I might go in, turn them all of, print a packing slip, then turn them all (that I want) back on and see if that resets it?
I just printed 3 packing slips with no problem - using my iMac and Safari.
It sounds like the buyer selected the "gift" choice when purchasing. The packing slip will not have any of the normal info or pricing on it. Nothing you can do about it.