As you told me not to do I bought an I2S bluetooth receiver. ;)
I programmed it and hooked it up to the Hifiberry DAC+ DSP.
I havent done anything in Sigmastudio but it just "worked".
(It is connected to the only input, DATA IN 2)
The settings of the bluetooth module are as seen in the picture.
First I haven't configured the I2S and second I haven't added it to the dsp program.
As I have tested, the Raspberry and bluetooth sound do get mixed up and played together.
Now what surprises me the most is that it runs without any configuration in sigmastudio.
I thought I have to add it as seen in the dsp program here.
Before I now upload this I want to understand it correctly.
After this test with the module just connected through cables and no configuration i am just not sure anymore that I have understood the whole system correctly.
Thanks for your advice and information!