Just got my Switch 2! Can I play Overwatch 2 on it? Is there a special version or just the same old port from Switch 1?

Yes, it's available on eShop right now. Same version as Switch 1 though, no improvements yet

The game runs on Switch 2 but it's literally the same version as the original Switch, so don't expect any visual improvements or better performance. Blizzard hasn't said anything about creating a dedicated Switch 2 version that takes advantage of the new hardware capabilities. The new Joy-Con mouse features won't work with it either until they potentially release an updated port. Still playable and you don't need Switch Online since it's free-to-play, but it's basically just backwards compatibility rather than a true next-gen experience

Works fine but don't expect any upgrades. Blizzard hasn't announced a proper Switch 2 version

You don't need Switch Online to play it since it's free-to-play. Just download and go!

Currently available on the eShop as the exact same port from Switch 1, so while you can definitely play Overwatch 2 on your new Switch 2, you're not getting any benefits from the upgraded hardware yet. The game will run the same as it did on the original system since Blizzard designed it to be compatible with both consoles. What's nice is that you don't need a Nintendo Switch Online subscription to play since it's free-to-play - just a stable Wi-Fi connection and Nintendo account. Hopefully Team 4 will eventually develop a proper Switch 2 version that utilizes the new Joy-Con mouse capabilities and improved specs, but for now we're stuck with the basic port.