mrior You are absolutely correct in your understanding of the BT1036C module's audio functionality. The module can be used as I2S <> A2DP (bidirectional) and also as I2S > Headphone/Speaker (output).
Regarding your question about GPIO control, your understanding is also accurate. In the standard released firmware, it is not possible to control GPIOs 2, 11, 13, and 37 via AT commands.
We fully understand the importance of flexible GPIO control in your projects. The feature you mentioned—controlling these idle GPIO pins via AT commands—is absolutely achievable through a customized firmware.
If you need customize a firmware, please contact the Feasycom sales you were contacted with.