I am a US citizen living in the US. My spouse, who is a French (so EU) citizen, is currently living and working in Heidelberg, Germany.
I am currently visiting him in Germany, I plan to return to the US in a couple months, but the duration of my stay here will exceed 3 months.
It is unclear to us whether I have to actively do something like apply for a residence permit (here, for instance, it sounds like I don't need to do anything). I only did the Heidelberg city registration (anmeldung) at the Bürgeramt when I arrived, also, my spouse registered me on his German health insurance (TK).
Can I get in trouble if I don't apply for a residence permit? Like, when I fly out in a couple months, will a German officer at the airport tell me I exceeded my stay, and what would be the consequences?