Firstly, a pretty great extension. I was considering starting coding one myself, but I don't think there's a point. I did think about a few other features though.

I'd like to have some stuff to be able to do filtering or analysis. These three things could perhaps in the battle history table, perhaps solely elsewhere where you can filter based on them:

- outcome of battle (knockout, forfeit, timer).

- how many mons were standing when battle ended, like in PS room tournaments: "Player X has won the match 2 - 1 against Player Y." Probably just the numbers suffice.

- how many turns the battle took

The point would be able to filter out battles which aren't relevant for analysis, like battles ended to timer on turn 1 (where applicable). Or forfeits on turn 1.

And regarding actual analysis... Instead of data on format level, it'd be quite neat to see how your specific team has done in matchups. Best/worst lead data is interesting and nice, but if it's just based on the species of the Pokémon and its details then it's bit shallow. Like yesterday, I built a VGC team and then played a few matches and tweaked it a bit. Then repeated that process several times. Now there's a bunch of data, but being able to break it down further would help to see if the changes were actually working.

In addition to team specific matchups, individual monster matchups per each individual of the team could be useful.

And I guess the extension could maybe pick the team's name from right before the battle is started, if the battle log doesn't contain the full team. Additionally/alternatively, manually adding tags to battles could help with that, and/or a few other interesting things, where automatic categorization could fail.