Welcome back to the Wefugees Community and thank you for reaching out to us.
Did you contact the immigration office (Ausländerbehörde) via Mail? If no, you should definitely send them an Email so that you can prove that you tried to get an appointment for the extension of your residence permit. Unfortunately, it is rather normal in these days that immigration offices have a high workload and procedures may take longer than they should. With the expired residence permit I would not take the risk and travel/leave Germany. The immigration office can issue a so-called "Fiktionsbescheinigung" (fictional certificate) in case the issuance of the renewed residence permit takes longer. With a "Fiktionsbescheiniung" you may be able to travel (depending on the type - please see this thread for more details).
Maybe a migration counselling office ("Migrationsberatung" or Flüchtlingsberatung" can support you in contacting the immigration office as well. Please let us know if you need help in finding a respective office in Frankfurt or if you have any further questions.
All the best,