It's long been settled that recording police in Germany is totally fine, but they keep claiming that once you have an audio track, it's recording "the spoken private word" which has special protection. Doesn't matter they're there in an official capacity, and also doesn't matter if you don't record audio. They'll just assume you are.
Even the press get targeted.
https://www.mappingmediafreedom.org/2020/10/02/reportit-poli...
ADDED: And it looks like there’s no out of the box way with the default iPhone camera app to record video without audio.
But the above is for private conversations. If the interaction is in a public area, then there isn't an expectation of privacy, so the number of parties informed is moot, but this has been the subject of legal disputes notably when it comes to police being recorded. If anything it would seem like government representatives would have less expectations of privacy when conducting official business, but it's been argued.