Sorry for the late answer [1]. I tried to explain it above, but the crux of it is this:
Should a site show up if it
- is pinned
- but isn't relevant (no mention of Firefox)
?
My guess based on first using Google happily for some years and the suffering from it second guessing me the next decade and seeking explanations is that something behind the scenes expanded <Firefox> to <browser> or maybe something even wider and then it matched.
Maybe this is correct for many and I should write Firefox in doubleqoutes to demand an exact match, but personally I write browser when I mean any browser and Firefox when I mean Firefox specifically.
Hope this helps.
[1]: which is a good sign because I haven't had any other issues with Kagi since February[2]
[2]: hich is a long time in my world, I had issues with Google on a weekly basis and DDG probably every day