Hi Jürgen,
In your initial post you mentioned that when you turned on it was looking for /lib/firmware/TIInit_7.2.31.bts file. So bluetooth should be present.
Also share the complete log when BT is turned on and steps used.
Are you using SDK prebuilt binaries for AM335x? You can try using the prebuilt binaries from
http://software-dl.ti.com/dsps/dsps_public_sw/am_bu/sdk/AM335xSDK/latest/index_FDS.html
Regards,
Abhijit