Well, I’ll give the mono font a spin, but I’m not sure what bothers me more - the different sizes or monospace font for reading 
I understand that since this bug hangs there for 5 years now we shouldn’t expect it to be fixed anytime soon?
And for the recrod. Here is what you have to set:
.CodeMirror, .CodeMirror-cursors, .CodeMirror-cursor {
font-family: "JetBrains Mono";
}
As you expected - it still doesn’t work for headers. My guess would be that it’s because the cursor is rendered outside the H* tag.