I think this is a deal-breaker. I want a password manager to track the counter for me - at which point why use hashes as passwords?

Yes, as I mention it on the website. Pashword is for people who do not want to use or maintain a password manager.

Pashword is a nice replacement when all you need is a strong password and don't have a password manager and don't want to remember too many things.

Most people have worse security than Pashword, which is: weak passwords + same passwords everywhere. Pashword overcomes that problem. It is not better than a password manager, can never realistically be but you can use it with a password manager, to store secret keys.

I appreciate what you are trying to accomplish with Pashword, but it would be better to direct people towards user-friendly password managers such as Apple Keychain (if they are in that ecosystem) or BitWarden.

I actually built it for my personal use and made it public because there might be people who are comfortable with such a thing.

It works great for me so I have no complaints, plus I got to learn a lot :)

and how do you keep track of the counter for each website?