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A paid Apple Developer account is not required to have binaries notarized.

Sadly it is required to have a paid account.

Sadly you have to accept PAID agreement to get notarization to work. https://mjtsai.com/blog/2019/10/17/catalina-notarization/

Can you quote the relevant paragraph that you have to pay to get an app notarized?

You already needed a paid account to get your apps Developer ID signed in the first place.

If you're not using Developer ID and instead expecting your users to bypass Gatekeeper, that still works in Catalina.

No, notarization is not required to run an app on Catalina. Gatekeeper is only invoked if the quarantine attribute is set on the file.

Browsers are supposed to set that attribute. If they don't then Gatekeeper won't be triggered.