What is Turkey's strategy

Turkey would LOVE to be rid of the Kurds.
There are lands on the Syria/Turkey border (encompassing both sides, but particularly to the SouthEast) that are essentially operating as their own mini-state, populated by Kurds. The Turks have been fighting a war against the Kurds (who want independence) for generations, but it's been more of a... silent war of attrition for much of that, rather than outright conflict.
The withdrawal of the US from northern Syria has allowed the Turks to take advantage and step into the void - forcefully.

What's the end-game?
I don't think Turkey's end game is complicated. They want the kurds dead, and they want to re-establish their authority over that land, which would likewise give them greater opportunities in Syria.
What's really odd right now is the relationship between Turkey and Russia. It's really love/hate. I suspect we can read too much into the Biblical text - there's not a great deal that says that Russia/Iran/Turkey will love one another when they come against Israel - they're driven by a mutual hatred, not held together by love.

It's worth keeping an eye on.