The button within this popup that says “Don’t offer to scan external devices” does not do anything. The popup appears every single time a thumbdrive is plugged in.
I don’t use Avast One but Avast Antivirus Free and the UI differs:
I’m looking at the User Interface - Menu > General > Notifications > Ask to scan external storage (which is unchecked in my settings).
Now I often connect external drives to backup my system and data, I also on occasion connect USB sticks and I don’t get this issue.
I would assume that you have a similar setting in Avast One, if you can find it and ensure that option (Ask to scan external storage or equivalent) is unchecked. I appears that this isn’t being reset and why you are getting it each time.