Bitwarden has been good for me, but I actually don't know about safari...

Keepass does a pretty decent job. I have keepassXC on my Windows, Debian and Android devices. On Android it's integrated into the phone(and the autofill service if actual 2fa isn't supported on the app) so it works on every application. With IOS though I know they can be a stickler on anything remotely technical so I'm not sure if something similar exists with it. I also use syncthing as the service to make sure the same copy of the database is on each device to prevent having to use a password manager that requires a subscription for a cloud service, this also minimizes my risk factor of a cloud service being compromised.

Heard great things about bitwarden. I’ve personally been using 1Password for over a decade.

For mobile safari Bitwarden (and I think a number of others, but Bitwarden's the only one I can speak to) ties into Apple's password management system for autofill and password generation. Still have to use the app or webpage (either Bitwarden's official site or self-hosted vaultwarden) for more in depth management.

For mobile Firefox, on iOS it's the same as Safari. On Android you can either use the Bitwarden add-on or use it with the app and Android's built-in password management system just like on iOS.

Since you mentioned "all browsers" for chrome/chromium based browsers there is also on add-on for both mobile and desktop. For Internet Explorer and pre-chrome Edge I don't believe there's an add-on but it can still work, it'll just be more of a pain since you autofill either won't work or will be spotty. You'll probably be relying on the standalone desktop app.

On MacOS it integrates with Apple's password management, so no need for an add-on on desktop safari.

For other browsers, you'll probably have to use the desktop app and manually copy/paste just like for IE.

I also remember seeing some third-party integration for the windows terminal app and various Linux terminals, but I can't really speak to their quality or functionality since I haven't used them. But that would probably cover your needs for terminal based browsers like Lynx.

Not an iOS user and it certainly seems like something they would be behind on, but with Android every password manager with a Android app will work since the hooks are built directly into Android. Other than websites and apps that don't implement passwords properly it works pretty well.

Bitwarden

Keychain should work in both now. (iCloud passwords)

I'm a big fan of the Keep It Simple (KISS) approach, and went with Password Safe. Works on Linux, Windows, MacOS, iOS, and Android. It's big thing is it just makes an encrypted password file which then you can sync between devices however you like (Box, Dropbox, etc)

Which one works on all browsers including mobile safari and mobile Firefox?

It has an auto-type and copy feature, so no need for browser support. Though, the main criticism of this offering is if you want a ton of features and don't care about KISS.

If there's one thing I've always been wary of, it's the password manager browser extensions. And I've been proven right. Don't be lazy, it takes 30 extra seconds to do it manually.

Pishing detection is nice though, I'll admit.