What is spyware to you? If it's spying on me without consent and sending private information about my computer it is definitely spyware, regardless of the database they use.

Since they don't ask for consent and uses PII, it is illegal under GDPR, probably CCPA and other laws too. It's also Not Nice™.

What private information about your computer is it sending? Browser, OS, screen size, location, ISP. Under GDPR, and the way i see things, none of that is PII.

It generates a unique identifier which it transmits on each invocation. The identifier uniquely identifies the installation of homebrew, linking all of those other bits of data together across time and space.