It is truly upsetting to see how few people use password managers. I have witnessed people who always use the same password (and even tell me what it is), people who try to login to accounts but constantly can't remember which credentials they used, people who store all of their passwords on a text file on their desktop, people who use a password manager but store the master password on Discord, entire tech sectors in companies locked to LastPass, and so much more. One person even told me they were upset that websites wouldn't tell you password requirements after you create your account, and so they screenshot the requirements every time so they could remember which characters to add to their reused password.
Use a password manager. Whatever solution you think you can come up with is most likely not secure. Computers store a lot of temporary files in places you might not even know how to check, so don't just stick it in a text file. Use a properly made password manager, such as Bitwarden or KeePassXC. They're not going to steal your passwords. Store your master password in a safe place or use a passphrase that you can remember. Even using your browser's password storage is better than nothing. Don't reuse passwords, use long randomly generated ones.
It's free, it's convenient, it takes a few minutes to set up, and its a massive boost in security. No needing to remember passwords. No needing to come up with new passwords. No manually typing passwords. I know I'm preaching to the choir, but if even one of you decides to use a password manager after this then it's an easy win.
Please, don't wait. If you aren't using a password manager right now, take a few minutes. You'll thank yourself later.
The passwords are stored locally. You can test this yourself by turning off your WiFi or disconnecting your Ethernet cable and then going to about:logins. All the passwords will still be there.
You can also test it by logging in to a new computer and getting all your passwords there too
Please don't confused this with backup as a sync could trigger a delete.
There are several Firefox tools that do things like this if you look!
You can (and probably should) backup your passwords. Same goes for any hosted solution.