When the mod Warp Drive Machine is enabled, the module insertion doesn't work into mining drills.
I only tested the electric furnace besides the mining drills and it works properly.
One thing to note is that the request works into mining drills ghosts. Just not in the actual drill.

So, as a workaround, I disable my personal roboport, place the drills ghosts and then use Module Inserter to request modules before enabling my personal roboport again so it works as expected.

This is caused by how Warp Drive Machine handles preventing building certain things in various places - and it ends up preventing the module requests created by this mod.

I could change my mod to prevent that event from being sent, and thus prevent Warp Drive Machine from having a chance to block it. I don't want to do that though, because some other mods do want that event (a previous thread (https://mods.factorio.com/mod/ModuleInserterEx/discussion/654686678513b3f6cf7cf79a) resulted in specifically adding the event, so it could schedule a spidertron to go to the location and build it).

So I think the solution is for the Warp Drive Machine mod to update and allow creation of the "item-request-proxy" entity type anywhere.

Thank you very much for your response!
I've created a topic about the issue on the mod page.