I have now bought a SkyConnect Stick and after several restarts of the smartphone and factory resets of the Tado X devices, all devices could finally be set up.
By the way, I had to do this too: Pure HA+Thread, "Border Router required" - #16 by WallyR
So maybe it would have worked with the Echo 4 after all. But for me it’s okay that I’ve now bought a SkyConnect stick because I want to gradually get rid of the Echos and Alexa anyway.
As @agners has already mentioned, all the additional functions are missing. For me personally, the window open detection would be enough as a sensor. Everything else can also be built with automations or with Better Thermostat directly in Home Assistant.