Note, currently BSW and FDP are both below 5 percent which means they won't get into the Bundestag which drastically changes the number of seats the other parties get. As long as they don't go over 5 % a coalition between the Union and SPD is possible.
Söder pretty much declared the Greens their main enemy. I don't think there'll be a coalition of CDU/CSU and Green in the Bundestag until CxU declares a new main enemy (why not AfD?).
Söder understands the difference between electoral rhetoric and Realpolitik and so do CSU voters. And theatrics. He can go "I'll keep an eye on those breaknecks, make sure they don't convince the CDU of anything stupid", occasionally make noise, and keep it at that.
The "main enemy" thing is absolutely true, of course, just have a look over the border to BW. But that's about state, not federal, politics, and as long as the CSU keeps ruling Bavaria they're happy.