Dear @AnneSo12 ,
If the family left in August, I presume their permits have now expired. They will have to re-apply when they re-enter Germany.
The core requirement to receiving temporary protection (paragraph 24) in Germany is that they were resident in Ukraine before February 24th 2022. They would therefore still be entitled to paragraph 24. I am not aware of there being issues for individuals who have let their permits expire. However, the application of this law is new and so we do not yet have experience of how it is applied under different circumstances.
As far as I can tell, it is still possible to register in NRW (I myself work in Saxony). As you have mentioned, some states cannot accept any more people and so transfer them elsewhere. If the family has the possibility to stay with friends in NRW at first, then it will help as they can register and get settled there. If they make use of the municipal initial reception centres, they will then be transferred to a part of NRW which still has capacity. This mean they could be separated from friends.