indeed, that worked.
I converted .exr to .hdr using gimp, than I put the HDRIBackdrop, I set size so big so my scene is included within the HDRIBackdrop and I had to select “SM_SkySphere” as mesh for everything to look nice. Again, there seem to be different ways to build a sphere from polygons or some other thing affecting the display of my texture.
But that’s actually nicer as my custom material as this plugin does all the work for me, including a skylight.