The SPD turned into a third way economically liberal party around the same time Tony Blair did the same to Labour in England

Actually, the SPD under Schröder did imitate Tony Blair’s “New Labour” strategy.

Remember it was Merkel from the CDU (alongside Swedish social democrats) that was the biggest proponent of humanity and solidarity when a bunch of asylum seekers arrived in 2015 - “wir schaffen das” and all that.

That really was just clever PR. Merkel originally wanted, following the party line, to close the borders, but since she isn’t stupid and a bit of a legalist, had that plan legally evaluated. The evaluation came out negative, because doing so would have been in violation of both German national and international law. Accepting the refugees really was the only legal option. So she did the next best thing she could do after failing to fish for votes in the far right’s disgusting brown cesspit, and sold the thing she was forced to do by having no other legal option as a humanitarian act of hers, to at least score some sympathies with less right leaning and more humanitarian voters.

The leadership of the CDU has taken a turn to the right since Merkel

Basically, they went back to their former self of outright right wing populism, and to brazenly and openly shitting on both national and international law, because they know exactly that nothing substantial will happen to them for it, the worst that will happen, is a court writing a sternly worded letter and invalidating a law that has been in force for as long as the court took to decide (usually many years).

Remember that the founding members of the far right AfD were pretty much all previous members of the CDU’s right wing. These two parties fit together like an arse fits on a bucket.