Curate, connect, and discover
“Is katara the fire Lord since she’s the one that beat azula” no. Duh. Azula forfeited the agni Kai by shooting her lighting at katara, so by the time katara beat her the agni Kai was over.
The real question we should be asking is if using dynamite and other explosives in an Agni Kai is allowed and in turn if sokka and toph can become join fire Lord. (Sokka uses the explosives, toph blackmails him into a joint leadership)