If the processing time for a residence permit application extends beyond the validity of the visa you first used to enter Germany and it is expected that your application will be granted, it is common that you are allowed to stay in Germany until the application is processed. If you need to formalize your status, you can apply for a fictional certificate (Fiktionsbescheinigung), confirming so. In your situation, you should be entitled to a fictional certificate confirming the continuation of your previous right to stay beyond the original expiration date (May 13th) according to § 81 Abs. 4 AufenthG. With a fictional certificate based on § 81 Abs. 4 AufenthG, you are entitled to travel to other Schengen countries as if you had a regular residence permit and both leave and reenter Germany. Be aware that it is important in your situation that the certificate is based on § 81 Abs. 4 AufenthG. Fictional certificates based on other sections of the immigration law may not allow you to travel to other Schengen countries or reenter Germany.
Even if there are not supposed to be immigration checkpoints at the internal Schengen borders, there are currently due to the 'refugee situation' still frequent immigration checks at the land borders when going from Hungary to Austria or when going from Austria to Germany. Without the fictional certificate, you are not unlikely to experience problems at the borders if you are going on your planned road trip. Even with the certificate, it is not quite unlikely that you are held for questioning entering Austria. Immigration officers from other Schengen countries are often not familiar with the German fictional certificates and may not immediately recognize your right to stay.