there is something soooo satisfying about seeing the outline get filled in, love this sooo much! Also I feel like X should be a government building/tax collecting? and Y should be some type of armory/fort.
i think the island to the right could be a fortified area of the city, and Y could be a fortress defending Kadjar, as i call it, to its east... but that would mean making a western island-area of Kadjar, with its own fort to the western-most part. not sure if you're fine with the idea of "Kadjar Cardinal Forts".
Y should be a temple to a pantheon. You already have a government building but not a major place of worship. Maybe the temple is to a wisdom/teaching deity for the academys The arena would be cool. X could be a government building...
Maybe for the university switch that to a huuuuge ship building yard. And that government building to the academy. And that other island an academy for just nautical schooling.
Y the emperor upper palace with the other palace being his more government meeting one and the other Y being more of a home/ceremonial palace with like a coven/magic system being represented