Firefox

If Chrome is at v162 and you’re at v3, people perceive the version numbers to reflect the quality and development.

I don't think it is the case. Ask some random person what version their browser is and they probably won't even know how to check.

It doesn't matter for the vast majority of people, the only people who care are power users. And what do power users appreciate? Clear communication. If there's a major UI change or something, bump the major version. If there's a new feature, bump the minor version. If it's just bug fixes, bump the patch version. Or even simpler, since Firefox has the ESR build, bump the major version whenever an ESR build is cut, bump the minor version every regular release (4 weeks?), and bump the patch version every patch release like we do now. That way I know how much the ESR build has deviated from the regular build, which is valuable information (just look at the minor version for the latest Firefox).

How you manage versions doesn't matter to the vast majority of people, so it should be tuned for the minority who actually kind of care, so make it mean something. A year would be fine and useful, a number that increases w/ the ESR refresh would be useful, an ever-increasing number isn't useful. Pick one of the useful options...