A password manager just helps you store your passwords, and automatically inputs passwords for you. This makes it easier to use a variety of strong passwords. Also the password manager can check for a domain name match before doing its automatic input, which helps provide phishing resistance.
"2nd factor" or "multifactor" essentially just means adding on something in addition to passwords. That could be in the form of:
* TOTP = "time-based one time password". Use an authenticator app on your phone to input a 6-digit code which changes every 30 seconds or so.
* "security keys" / "hardware security keys" -- a dedicated device that allows you to authenticate, e.g. via USB or NFC. Generally considered more secure than TOTP, because the code is more than 6 digits worth of entropy, and also it forces the website requesting the code to authenticate itself before it provides the code (again, helps with phishing resistance).
I don't know anything about passkeys or Windows Hello.
As for backup, you should be able to transfer all of your TOTPs from one phone to another by scanning a QR code. For hardware security keys, you can buy multiple keys, register all of them, and keep them in different places. Then if you lose one you just use one of the others (and register a replacement to maintain redundancy).
For the TOTP, if you're worried about losing your phone, usually when you set up a TOTP you can also copy down some single-use "scratch codes" that can work as a backup if your phone breaks or something like that.