For my part, I'm pushing as hard as I can to replace Chrome on everyone's machines with Firefox. It's not even the same game any more though.
In the 90s there was still a fighting chance — and we won! — because the technologies at play were not entrenched in every day life. Now it's more akin to replacing every car with an EV.
But in this particular case I think that different browser (or particularly Firefox) would not possibly prevent that problem, since (Firefox) shares same "Safe Browsing" database with Google, for "Phishing Protection".
This. Firefox even sends the hash and filename of each download to Google. So if you use Firefox to download the Tor browser, an abortion price list or a secret PDF, Google knows you downloaded it.
https://www.pentagrid.ch/en/blog/block_browser_requests_to_g...
Disclaimer: The blogpost is two years old, but I assume this is still current.