Does it work like that? Everything I see says they’re tied to that device.

It depends on what kind you want to use. If you want the most security, you can store them on something like a Yubikey, with it only being on that device and not exportable. If you get a new device, you'll need to add that new device to your accounts. For less security but more convenience, you can have them stored in a password manager that can be synced to some service (self-hosted or in the cloud) or has a database file that can be copied.

Fair, I guess I’ve never lost a password because it’s just a text string in my PW manager, not some auth process that can fail if things don’t work just right.

That's fair. It can be a bit of a mess with different browser, OS, and password manager support and their interactions but it has continued to get better as there is more adoption and development.