I don't know how Mozilla even exists financially. Is it just that Google keeps them alive to avoid antitrust lawsuits against Chrome?

Pretty much, about 85% of Mozilla's revenue comes from Google in exchange for making them the default search engine. The ongoing antitrust case against Googles search business is threatening to make that deal illegal though, so ironically the attempt to break up one Google monopoly might incidentally kill Firefox and make another Google monopoly stronger than ever.

Assuming donations would still be legal they have the funding structure to get around that through their foundation.

They are gonna need to shed a lot of weight (like this project) in order to make donations feasible.

In a separate comment, I mentioned how Mozilla should have been more like Proton with their cloud storage, VPN, password manager, and cloud office suite.

In fact, they should have done that a decade a ago.

Mozilla has been around since the late '90s and should have evolved beyond just being a browser company. They launched a VPN service when VPNs were already everywhere, and they did the same with a bookmark manager when others were already offering similar solutions. Mozilla is always catching up, never leading, and that's a common issue with many big open-source and free software companies. They often pretend to be a business that isn't heavily propped up by big tech donations.

If I were leading a browser company, my focus would have been aggressively directed towards small business software. I’d create an internet and privacy-focused affordable minimal business software suite that lives within the browser — a combination of Proton and Zoho. And I’d strongly avoid building things that should be browser extensions.