I just came across this issue myself. After I cleaned out some old Boarding Passes, I only had one Pass left and noticed the "Edit Passes" button had gone missing.
Online search showed me others had run into this - but I did not see any solution https://discussions.apple.com/thread/250836037
Because I remember seeing the "Edit Passes" button when I had more than one Pass in my Wallet app -> I added a Grocery Card Pass through the Grocery Store's App and voila -> the "Edit Passes" button is back.
In summary: "Edit Passes" button only shows if you have more than one Pass in your wallet. That's a bug. Looks like the difference in layout between one Pass vs multiple Passes inadvertently appears to bump the "Edit Passes" button down and off the screen. There is no swiping that can get you there.
Now I can go and scan the QR code that I wanted to add to my Wallet app in the first place.
