There’s stuff about “that situation” I don’t know, haven’t investigated, so who am I to comment.
On SE I would like to do as little as possible (acting as a moderator, reproving rude users, is tedious; fortunately the large majority of users don’t require my moderation, in my experience, i.e. they’re moderate already).
Initially on SE I’d post a comment to @ the user. My comment would reference some specific sentence[s] of the Help or FAQs or CoC which they seemed to be ignoring when they posted their comment.
If it happened again, after I tried that once or twice, I’d begin to delete those offending comments without further comment.
If it still continued then I’d send a mod message, quoting the actual latest comments of theirs which I found unacceptable, and quoting the Help/FAQs/CoC again.
The next mod message after that should come with an timed suspension of their account (then escalate if still necessary).
I am inclined to agree with Monica’s dicta here.