Microcontroller-boards for entirely wireless charging battery pack

Yeah, but there are magnet phone cases (for other purposes) that work with Qi-chargers. So I think that part is more about proper alignment with which the magnets could help.

However, I‘ve only seen ICs that either manage Qi-reception or Qi-transfer... I‘m wondering how difficult it is to build a PCB that can do both since I have no experience in this field at all.