Open Settings, scroll down to Spotlight. Unselect the things you don’t want.

You’re welcome :-)

Just noticed that I was sharing my entire Safari, Spotlight and Siri search history in that menu. Why is that setting in Spotlight settings and not under Privacy/Analytics?

Because spotlight indexing is local and not shared with Apple?

Like I pointed out elsewhere, it doesn’t stick for me.

I've found that kind of thing is often caused by a damaged preferences file. The easy way to check that is to make another user account, and see if it happens there too.

Thanks!