If I want equalization or convolution I apply them upstream shortly after decoding.
I don't think major music listening apps will switch your EQ automatically settings based on your listening device. So either you are doing that manually every time you switch devices, or you set your headphone EQ directly.
In any case, the software around this is not clean, and has lots of room for improvement.
I’ve had to set EQ on Bluetooth speakers themselves that didn’t sound so good out of the box.
Though at that point I rather throw away the speakers and get better ones…