There are multiple ways the Kagi favicon differentiates itself from the big G.
For one it is in minuscule g cf. the majuscule G. That should already be decisive enough.
Then there's colour - the big G uses a variety of primary colours. Meanwhile, Kagi's favicon seems to use black text on orange; or white text on purple.
I think the pathological association of any form of the letter gāregardless of its case, in any colour or formāto Google is not really contingent on Kagi.