How bad is Idea of .Zip as password manager?

I suppose there's nothing wrong with it when the file is at rest, it looks like zip uses AES 128 or 256 which are adequate if you have a very strong password for the encryption. Ideally the encryption would feature a computationally intensive algorithm to slow guessing attempts when attempting to decrypt so you probably don't want to use a weak password.

Usability won't be great, you'll be copy pasting constantly and that presents an opportunity for malware to spy on the paste buffer and steal your passwords but it's a low to medium severity issue.

If you want to keep everything local I'd recommend KeePass, it's free, open source, and very strong. It's kinda the same thing but with the ability to insert passwords directly in some cases and can do more to keep everything organized.

If you want to use this in environments where you can't install anything on the systems but don't want anything online, this is probably acceptable though.