It most definitely does, such as Google Calendar event alerts at least under Chrome. I'm not sure why it doesn't have unobtrusive desktop alerts instead. I'll have to take a look later to see if that's an option.

There is an option in Google Calendar under settings -> notifications -> Use browser notifications instead of interruptive alerts

Chrome on macOS always drove me mental, because of their absolutely terrible and reimplemented notifications system. Drove me batty. Nowadays I browse in Safari and develop in Firefox and Safari, so I don't know if it still does this

They actually switched to native notifications as of about two weeks ago.

I'm still on an older version of Office and it has it's own alerts system that I can't control. Maddening.