Thank you for your help!
In the meantime I was able to test both the Headset with other phones and my FP3+ with another Headset from Bose.
The results are:
I was able to use LDAC and AAC with the Sony headset connected to other phones. I was also able to use AAC with the Bose headset connected to my FP3+. I am assuming that Lineage OS would solve this issue, but from what I can tell I would have endless problems with banking apps and Google Pay.
So in conclusion:
- My headset does support AAC and LDAC
- The Fairphone 3+ supports AAC but refuses to use AAC with this specific headset
I will contact Fairphone Support with this issue.