@hmnd Thanks for finding the bug! I "followed" it; that seems to be the only way to +1 it without commenting (which I didn't want to do since I don't have any new information for them).
The way it's marked with Priority: P3, Severity S3 is not encouraging.
One point from the bug is that this only affects Manifest V3 extensions. I'm not sure whether Manifest V2 extensions are less buggy or always ask for more permissions.
@Vlad I understand your reluctance, supporting two extensions is more work. I don't know how much more work making a "Kagi Lite" extension would be.
For the one data point that is me: I realized that I don't have any other extensions that use this notification in any useful way, so I think I can get used to it. So, at the moment, this seems like a minor annoyance I can get used to, and I might not immediately uninstall the extension (haven't yet, at least). However, once (and if) I find another extension where this green dot provides useful information, I'll uninstall the Kagi extension.
One other thing you could do is to provide better instructions on how to use Kagi on Firefox without the extension, with something like the "Search Engine Helper" I linked to above. Unfortunately, AFAICT Firefox does all it can to make this tricky and unpleasant (but fortunately not quite impossible). If I try it out and have any thoughts on what those instructions could say, specifically, I'll write them down here or in some other Kagi forum.
And by the way, thanks for working on Kagi, I'm enjoying it quite a bit!