I dont think you need a Boolean at all, here. You can just use the holes Extra Objects > Honeycomb has given you.
If you work in the flat:
- Take 2 chunks of honeycomb ( to be more non-destructive, you could work under a Mirror modifier)
- E Extrude various edge-loops, something like as shown, and scale them to 0 in the appropriate dimensions to straighten them
- Cut some loops in the extrusions, to make the transition from hex to rectangle nice and even. I used the shipped Loop Tools add-on > Space to get an even distribution of vertices in the regions you want to be smoothly cylindrical.
Then you can give the sheet Simple Deform > Bend through 360, Weld to seal up the seam, Solidify for thickness, a Bevel modifier to put some glint in the edges, and smooth then out a bit...
The boolean modifier is cutting through the mesh, you just can not see it. You have to hide the mesh that is cutting through the mic (in your case those circles) in the viewport and the render by clicking the eye and the camera button or going to object properties>visibility and untick show in viewport and renders. For the smoothing problem you have to enable auto smooth.