I had actually created an issue with the main vim project on this here:
vim/vim#12952
I believe their assessment of this is incorrect. Within a double quoted string something like "\$somevar" correctly does NOT get highlighted as a variable, whereas within a HEREDOC string it does. Thanks!
EDIT: One thing to note: In the other issue I'd mentioned that this worked as I expected at one point, but I can see now that's in fact not the case. Those are highlighted as variables even in very old versions.