Bandle City and Demacia have a very weak link, so what does Poppy do as ambassador to Demacia? Yordles don't sound like the people that can see Demacians eye to eye, and we haven't even had evidence of their cooperation since old lore.
Based on old lore, she might have provided a Yordle's perspective in discussions and meetings; be the one to receive and guide Bandle City delegates visiting Demacia or Demacians visiting Bandle City; and occasionally use appropriate force if a situation deemed it necessary.
Yordles and Demacians may not agree on many subjects, but that doesn't mean they cannot have or attempt to foster a mutually beneficial relationship between city-states.
Compared to the likes of Noxus and Zaun, Bandle City probably doesn't seem bad. Sure, they have a bunch of weird customs, weirder inhabitants and convoluted contraptions, but they aren't evil folk. There is no sense in Demacia being hostile towards Bandle without reason.
Easy, she hammers out any relationship problems (pun very much intended).
She does things that aren't seen in the lore and won't be added to the lore with the lore team that Riot currently has.
She does diplomacy and sometimes aggressive negotiations.
