Value7609 can you make a screenshot? are you talking about the button on the home page of google.com? I don't think this is a problem at all because most of the people on Firefox will not go to kagi.com to do the search, they will use the search bar directly.
Assuming you are using chrome and doing a search on a smartphone.
- Main page of google. There is a chance to press the button by mistake
- Pressed the search bar, the keyboard will open, there is still a chance to press the button (but I mean, why did you opened the search bar in the first place if not to type on the keyboard)
- Entered any character. The mic button will disappear!
Btw, I would disable the Firefox button if I could too, the problem with firefox is that they make the url bar too short just to fit the mic button there, making cursor movements with the fingers difficult (which I suppose is similar to your issue). But adding the mic button to kagi.com won't affect that.
Anyways, I see most of the value in implementing it for the desktop version, which is where usually doesn't have any SST service.