Is there any prove for Googles influence on their development you outline here?
There's no world in which 75% of your revenue coming from Google doesn't influence what you do. Even if it's not the main driver of all decisions, pissing off Google is a huge risk for them.
Why would there be any proof?
Google is not bribing Mozilla...they probably keep them alive to avoid all kinds of monopoly lawsuits. With their market share however, you would need more prove to justify further conspiracies...
In 2021 they got $500M "royalties" (this is their payment from Google) with only $75k revenue from all other sources, including $7.5k donations.