The browser extension(s) utilize the wrong Universal Link format of 1Password to open and edit an item in the desktop app, and because of this, nothing happens when you click the "Edit" button. I played around with it a bit and, using the documentation from 1Password's own website, I managed to figure out the issue. I've included the link format that doesn't work, as well as my corrected version that does work. This issue occurs in Chrome, Edge, and Firefox.
First, the one that doesn't work (and is being used by the Browser Extension):
And here's the corrected version and format that I tested:
Note: There are exactly two reasons why the incorrect format doesn't work.
1) In the incorrectly formatted version, "edit-item" is in the URL, when it should just be "edit".
2) There's an unidentified ID immediately following "edit-item/", but when I erased it and used only the vault ID and the item ID in the URL, it finally worked.
1Password Version: 1Password 7.8.3.BETA-0 (70803000)
Extension Version: 1.25.6
OS Version: macOS Big Sur 11.3.1
Sync Type: 1Password