I’m not in Germany but as it’s in the EU I would contact a German employment lawyer.
Write a short summary of the events, detailing what they should have paid you, when they should pay it, what they did pay you, when they paid it, and how much they still owe you. Also include a copy of your contract.
Use bullet points and make it as easy to read as possible. Imagine you’re asking a stack overflow question.
Probably the lawyer will give you a free initial consultation where they tell you the next free steps.
Maybe the lawyer will charge you a few hundred euros to send a letter before action.
If the company doesn’t pay, and is still solvent then the lawyer might recommend taking them to court as the company will have to pay the lawyers fees if you win the case.
It’s likely your case is open and shut and it’ll never go anywhere near court.