They are totally necessary - if you don't use the same passwords across the internet I mean.
How many accounts do you have on the web? I can count at least twenty accounts that I have and use from a variety of services. Keeping different usernames, emails (through alias) and passes in mind is no easy task, so a good password manager is absolutely needed.
People are recommending Bitwarden and I can't say it's bad, truly, it's a really secure and private alternative. Although, in my opinion, keeping a offline safe for your accounts is way better because only you have the absolute control over all the credentials. I use KeePassDX on my PC and phone, synced by Synching, and being loving it for some years still.
The only Chromium based browser for android that I know can run extensions is Kiwi, most of webstore extensions works well on it.