Welcome back to the Wefugees Community and thank you for opening this important topic!
Indeed, the so-called traffic-light coalition (referring to the colours representing the three parties) is planning to introduce many positive changes and improvements in residence law and asylum regulations. PRO ASYL presents the most important points very well on their website. The source is in German though. Here you can read, for instance, that people may apply for a permanent residence permit (Niederlassungserlaubnis) after three years of holding a temporary residence permit and for the German citizenship after 5 years. As far as I understood, children born in Germany may get the German citizenship if one parent is staying regulary in Germany since 5 years. The Dual citizenship will be introduced (so far only applicable for EU citizens, for instance) as well.
Infomigrants published an article in English, also mentioning some of these aspects.
Regarding your individual situation being enrolled in an Ausbildung and still waiting for the asylum procedure result: The so-called "Ausbildungduldung" for rejected asylum seekers may turn into a residence permit.
I hope this helps and please don't hesitate to get back to us with any further questions.
All the best,