Bari was a duchy whose inhabitants spoke a dialect of Algarvian. It had been an independent entity in earlier history, under feudal conditions. However, in more recent times it was incorporated into Algarve and its inhabitants - sharing in Algarve's aspirations to become a major world power - were content to have it that way.
In the aftermath of the Six Years' War, the victors detached Bari from Algarve and set it up as an independent state under Duke Alardo - a step taken with the explicit aim of punishing and weakening Algarve. Therefore, the inhabitants of Bari disliked their new status and did not relish being "independent".
When Alardo died without issue, King Mezentio of Algarve took the opportunity to invade Bari and re-annex it to his kingdom. He encountered no resistance in the duchy itself, whose inhabitants welcomed the Algarvian troops as liberators - but he aroused the anger of the other nations, and set off the Derlavaian War.
Following incorporation into Algarve, inhabitants of Bari were conscripted into its army and shared in Algarve's initial string of victories, in the persecution of Kaunians and eventually in Algarve's downfall and post-war occupation.
"Bari" is the name of a city and province in Italy. Much like Algarve, the names of people and places in Bari are Italian.
Bari's role in the Derlavaian War is roughly similar to that of Austria in World War II, with the annexation being a close analog of the Anschluss. However, its role of "triggering" the large scale conflict more closely resembles Poland, which is otherwise analogized by Forthweg.