Forgive my ramble for a moment please. I’ve always thought the best Jar-Jar scene in the movie is when he’s talking with Padme while they stare out the window. “Gungans getting pasted to eh?” He’s empathizing with her and the viewer can sympathize with that. But he’s still not really doing anything in that scene. He doesn’t even actually suggest using the Gungan army. Just a casual comment from him. Still, he’s talking to her, he’s feeling for the people, it’s an okay scene.
The worst scene (for me) is him randomly stealing the bbq from the vendor and just tries to whistle it off. Where the hell did that come from? Just what?
Giving him agency (if I’m understanding Eddie correctly) would be making what is there of him more like example one and less like example two.