See my response a few comments down this thread. I found the counter and password-template too. I don’t have an iphone so I can’t test the app, but I very much think this app stores the ‘settings’ (counter, template) to generate the password. Based on what the api and CLI can do… it has to, surely. It also has the ability to retrieve a custom password.
Of course the webapp in the link doesn’t do all of that. You’re stuck with 1 password in 1 format. Unless you change your secret and then all your passwords change.
I’m not the person you’re replying to but I have a fun answer for how I did it before I moved to password managers.
I used to have just a single password, normal-ish password. Reasonable length, some numbers in there, random caps. But in order for me to have unique passwords on every site without losing track of all the passwords, I added the first and last letter of the name of the service at a specific point inside the password. My password was cryptic enough that if you would see it you wouldn’t immediately notice it. But for me it meant I had a single strong password that was easy to remember and unique for every service.
I’m still kind of proud of that one, even though I don’t use that method anymore.