Given your ticketed itinerary does not require entry to Brasil, I can't see any requirement to satisfy that country's entry rules.

Had you been transferring between separately ticketed flights at GRU, then BA would very likely expect you to carry the documents required to enter Brasil. But you are not: you are what's becoming a rare animal - a passenger in international transit.

Hoewever, with only 5 months left on a passport a lot of the world becomes closed, so maybe it's a good time to renew.