Stick twirling is great fun.
My most used trick is flipping the stick backwards as I lift it up; I believe this is sometimes called the "gospel twirl". It's a really simple and effective little twirl that doesn't mess with your grip and is quick enough to do while lifting the stick off a snare hit or crash.
I also like the fake twirl, but I'm usually not comfortable enough to do that between hits.
Here's a clip from an old music video shoot where you can see the gospel twirl in action. Once the snare backbeat comes in, I do it a few times in a row when lifting my left hand off the snare
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You can also kind of see it in this video, but the light show makes it hard to make out what's going on. It's a nice display of my rock moves in general though: Stick twirls, big arm movements, alternating hands on crash grooves, crossing my arms to hit two crashes and just generally pointing at the audience to get them engaged. We're on stage to entertain, after all, so it's important to never look boring or bored. Stick tricks can be a great tool to achieve that; it's no different than any other "rock moves" that other band members do. The difference is that they're standing up and can strut around, while the drummer needs to do other stuff to look cool.
Edit: I actually do a long fake twirl before I start to play too, I just noticed, at around the 14 second mark. The gospel twirling is probably most visible after 3:50