I had a major medical emergency during a UPSC cycle — does that exempt me from counting the attempt?

Tragically, no general medical-emergency exemption exists. The Supreme Court in Rachna v. UoI (24 Feb 2021) and again in 2021-22 rulings refused to toll the attempt counter for personal hardship, including COVID infection. Your only real lever is the WITHDRAWAL WINDOW (Mar) — if you can use it before the exam, you preserve the attempt; if the emergency hits after Prelims, the attempt counts.