[Update #2]: Shadow Warrior 3's pre-launch preview shows off wacky enemies, bad jokes and loads of colorful explosions!
[Update]: It's official, Shadow Warrior 3 will be launching on March 1, 2022!
Shadow Warrior 3 was originally supposed to be released at some point in 2021, but due to the team needing a bit more time to "sharpen its blades" it ended up getting pushed back to early 2022. While nothing has been officially announced since then, the freshly updated pre-order bundle on the Microsoft Store now lists the new release date as March 1, 2022!
Before you start making any sort of plans, it's worth mentioning that this could simply be a placeholder date. I personally doubt it as it's a bit too close to offer the Microsoft Store much leeway to work with, but it's still a possibility and so I would recommend against getting to attached to this specific date.
As for what exactly you can expect to see once Shadow Warrior 3 launches, that you can get a pretty good idea of through the rather lengthy "Way to Motoko" gameplay preview. It's a little bit outdated by this point, but it's still quite informative. Have a look:
Once we get an actual release date, and hopefully another one of these chunky previews, I'll make sure to let you know. Until then, you can read more about Shadow Warrior 3 over at Steam.