Hi @Malcolm
Based on the information you provide on your sister's situation, in my view the reisdence permit 25b would be the best option for her. I am assuming the child does not have German or EU nationality.
She must first apply for a Duldung for herself and child, now that her case has fully ended. Once she has a Duldung, she mostly fulfils the requirements for 25b, as long as she has or does the 'Leben in Deutschland' test also. The requirement of financial security is not necessary if she is a single parent with a child under 3. If she is not a single parent, then it depends on the broader family financial situation. Here is a good overview on the requirements for permit 25b:
https://fluechtlingsrat-bw.de/wp-content/uploads/2020/12/2020-10-29_Zielgruppenflyer_25b_3.0.pdf
As she has a degree and very good German, she could also apply for a qualified job and get the permit 18b. The advantage of this permit is that she could get permanent residency after 2 years. However, for 18b she would first have to leave the country and go through a visa process.
Best,
Éanna