Get a password vault, period. Most people choose bad passwords to start with and don't write them down.
I prefer BitWarden and pay the $10/year because it lets me share passwords with my Partner, children, and in-laws. It lets me designate Partner as my recovery, which means if I am inaccessible for a month, it unlocks for Partner without needing a one-time password.
There are others, but don't trust browser password saving and make sure you can access your passwords without your phone. This is because it might be destroyed in a car accident, lost in a river, or taken for evidence. You need to make sure there are at least two different ways to get to the password.
Also, use a good password for your vault. I like phrases and sentences instead of random letters. As XKCD points out, it is easier to remember “behold I am made of cheese” instead of “a8$jd8298vlk#$” but they have the same basic strength. It's a pain to type though, but you can use biometrics if you feel that is safe.
As a first day item, the directions in your file should explain how to get into the password vault. That allows you to change your passwords via the vault and not have to write down every password change you make.
Use authenticators whenver possible instead of SMS. Ideally, the authenticator should have a backup and multiple access. The reason to avoid SMS is because it requires a phone, which may be lost or inaccessible when they need it.
I use BitWarden for the bulk of my authenticators, but I also use Ageis for some critical ones because it is not automatically shared across machines.