How can I tell if a spyware alert on my iPhone is genuine?

You just saw an advertisement and it was not from Apple. These types of ads are more frequent on sites that are considered to be less than legitimate. Any such ad is just an attempt to scare you into downloading software or call a fake support site to try and get your personal information, which will result in your account being compromised or even your financial information if that was given to them.

That alert was not from Apple. It's an ad from a website trying to scam you into buying something. Ignore it and consider not visiting that web site anymore.

You saw an advertisement. Not a notification.

Probably an advertisement for a “coffee shop” VPN, or some other unnecessary and problematic app.

Here is the Apple notification info, including how the notification is shown:

About Apple threat notifications and protecting against mercenary spyware - Apple Support

Some background on spyware:

https://www.wired.com/story/apple-iphone-spyware-101/

Scam advertisements are far more common, including fake “scans”, and fake “virus” warnings.

Such "alerts" are typically from scammers.