At first sight, I don't see how the FOIA is much different to the Informationsfreiheitsgesetz (freedom of information law). https://de.wikipedia.org/wiki/Informationsfreiheitsgesetz
Isn't the FOIA also applied on the federal level?
> In Germany, you are generally not allowed to film law enforcement
I think this is misleading. It's not especially prohibited. Generally, law enforcement enjoys the same rights as everyone else, that is having a right to privacy and the confidentiality of the spoken, non-public word. You can't film law enforcement folks preemptively, or without cause, if they have the reasonable expectation of confidentiality of the spoken word. If law enforcement is breaking the law, you are allowed to collect video evidence. In any case, you are not allowed to publish non-public video recordings or pictures of anyone, taken without explicit, or implicit consent. Public or non-public here means the implied confidentiality of communication, not necessarily where it happened. Eg. talking on a public street doesn't make every conversation public.
Mind you, in Germany, illegally obtained evidence isn't as easily dismissed as it is in the US. If you record the police without cause (illegally) and they happen to commit a crime, your recording isn't tainted evidence as far as I know, but rather you may (if indicted) face legal consequences yourself, independently. Again, publication is a completely different matter.
Legality of video recordings is pretty much irrelevant, regarding the legal power dynamics you described, as the police could just confiscate your phone and find some excuse for destroying the evidence. Independent oversight seems more important to address this.
On the other hand, I do think law enforcement should enjoy privacy, generally, as everyone else. I don't think, having a camera in your face with every interaction is helpful for anyone, all things considered, but would rather aid escalation and discourage leniency. Constant video surveillance just sucks, no matter who is doing the recording.