I wonder how many password managers, besides Keychain, allow you to autofill without the use of a web browser extension. Codebook, which is what I use, has a Mac extension that works with Apple’s Password AutoFill to autofill in Safari. (Edit: To be clear, Codebook uses an extension to work with Apple’s Password AutoFill, but it isn’t a browser extension.) However, if you prefer not to use any extension at all, you can use Codebook’s helper application (Secret Agent) to autofill in any browser.
I try never to put a password on the clipboard because of the security risk. With Secret Agent, I can copy data in Codebook into any browser or any other location (e.g., the password field when mounting an encrypted drive). 1Password and likely other password managers also have this capability.