I slacked off and went to sleep last night with this Suggested Edit review pending on my screen.
When I returned this morning, I voted to reject the proposed replacement of tag "proof-writing" by "fake-proofs". There was already one vote to reject when I cast mine, as "conflicts with the author's intent", so I was surprised to see the red box pop-up informing me that the edit had already been approved! That's the price paid for falling asleep!
Anyway, not to rollback without discussion, the current text of the tag info for "fake-proofs" leans into the notion of "Seemingly flawless arguments are often presented to prove obvious fallacies (such as 0=1)."
In this Question the issue is rather one of an incorrect proof of a true result (not of an "obvious fallacy"), namely that squares of real numbers are nonnegative.
As with many discussions Martin Sleziak was there first with this meta Question, What is the best tag for "spot the mistake" questions?
The other tag Martin mentioned in the older discussion was "solution-verification" or "proof-verification", noting the drawback that in these situations is aware that a mistake exists and is not asking for confirmation that a proof/solution is correct. Jyrki made a Comment there that perhaps no special tag is needed for such Questions beyond the subject matter itself. The original tags for the reviewed post were "proof-writing" and "logic", which seem appropriate even if one might accept tagging with "fake-proofs".
My question is whether the "fake-proofs" tag should be strictly limited to cases of obvious(?) fallacies. If not, then presumably the tag info should be updated to acknowledge the expanded scope of wrong proofs of true statements.
UPDATE: I replaced the "fake-proofs" tag on the linked Question with the "proof-verification" tag, and I made slight edits to both tags to reflect the slight sharpening of scope per the voting on this post.