Power is usually not absolute, at least in modern societies. So while it’s an open question whether Afd will become part of either state’s government, they will most definitely gain a lot of power and they will use it. It’s very likely that they will be able to veto anything that needs a 2/3 majority, such as appointing constitutional judges or changing state constitution.

E.g., in Saxony, the existing coalition wanted to protect courts better and add sustainability as a goal of the constitution. Even if CDU were to stop blocking those projects, neither would be realistic after this election.

CDU also won’t be able to govern properly with BSW, even as Eastern parts of the CDU are quite Putin-friendly. BSW uses a casting process led by Dear Leader’s which makes it likely they’ll leave seats open again (as they did in the past local elections). Also, Dear Leader defines all political goals herself and it’s completely unclear whether governing in Saxony/Thuringia is one of them at this point in time.