Your particles are too small and or not moving fast enough to make a noticeable impact on the smoke simulation. You can visualize the velocity field in the pyro ‘Smoke Object’ node in your dop network. You can see they're making a small dent in the smoke sim. Hard to see in the viewport, but might be visible in render.
Thank you reuben94. I have completely rebuilt the setup again. This time I did not use the satic object node anymore. Instead I converted the particles to VDB and added them as volume source / collision to the pyro setup.
For all who are interested here is a gif and the project file.