Gray overlay and no dialog when clicking Image button in CKEditor
After discovering that the Image button works fine in the default "Advanced" text format, which I did not modify, and which doesn't have the Media button added, I started investigating differences.

Turns out that if I disable the Picture module in Editor Appearance > Plugins, things work.

I just don't know what I'm giving up by disabling this. I would like images to be responsive. :-(