I could be mistaken, but I’m pretty sure all donations go to The Mozilla Foundation. I believe the foundation is the decision-making power for the corporation.

Either way, yes, Mozilla sold their soul to Google (specifically, giving preference to Google Search) in exchange for sustainability (read: survival). Rather difficult to compete in a market where Google and Apple collectively hold upwards of 85% market share for something they provide “free.”

https://gs.statcounter.com/browser-market-share