3-3 invasions are totally a thing in 9x9. They tend to pop up most in the connect variant of the Black Boomerang opening and in the Flower opening. I wrote a bit about both openings and 3-3 invasions specifically in my book, Mastering Mini Go.
But honestly, you’ll probably get a decent feel for them by just browsing the variations in those opening books to see how they can play out. You can also see what humans are doing with a database like Go 9x9 Opening Explorer. You’ll just need to click around until you reach a position like those above where a 3-3 invasion is realistic.