The easiest way to get the easy of use of Safari's password manager in a different browser would be to use a different password manager that works in other browsers. Common recommendations are 1Password (my personal favorite), BitWarden, etc.
This might not fulfill your needs though, since it sounds like you'd like to use the Safari password manager in a different browser, which is not possible outside of the Chrome extension [0] that Apple provides. This means that it wouldn't work on Firefox.
Apple has an extension for Chrome ("iCloud Passwords") that lets you use the keychain passwords there, but nothing for Firefox. It's less-restrictive than it used to be, since the extension used to only support Chrome on Windows, but they gave in back in July of this year and made it easier to use Chrome on Mac.
Apparently, Firefox removed a bunch of password-related APIs back in Firefox 57 that broke some existing keychain extensions[1], so it might not be Apple's fault that they've not provided a Firefox extension. There's no progress on Firefox bugs related to making such an extension possible again, that I could see.[2]
This might not fulfill your needs though, since it sounds like you'd like to use the Safari password manager in a different browser, which is not possible outside of the Chrome extension [0] that Apple provides. This means that it wouldn't work on Firefox.
[0]: https://chromewebstore.google.com/detail/icloud-wachtwoorden...