TLDR for anyone else running into this: Type auth.mangadex.org into your URL box and hit enter, then disable it for this subdomain as well.
Apparently it also has to be disabled on auth.mangadex.org, or at least that's what I'm hoping since I just had it happen again. Hopefully this will be the end of it, and there aren't more subdomains to disable it on.
It wasn't obvious this function was accessing auth.mangadex.org (which might be why Privacy Badger treats it as suspicious)... as far as I can recall just now, the "You need to sign in to access this page" (with a button that lets you do so) page doesn't display it in the URL. But when I officially signed out and officially signed in, the URL box did include "auth." so it was easy to disable it.