So what kind of government does the Timurid Empire have?
Is it a Yugoslav style federation built on absolute rule?
How do Central Asians feel about celebrating a genocidal monster?
The Timurid Empire is a confederation of many central Asian nations, which vary from absolute monarchies to republics. For the most part, the subdivisions are allowed self governance, but foreign and military Affairs are handled entirely by the national government and the head of state does have a rarely-used veto on internal affairs.
Their is also a middle tier of government, roughly equivalent to the old SSRs. These are run by Mirzas, a term that roughly translates to governor but isn't a similar position, and is closer to US senator. The Mirzas form the national parliament and elect a chancellor, as well as appoint an Emir from the local nobility at the death of the previous Emir. Officially, each Mirza is devided into Oblasts which form the local government, but these rarely exercise much power. Instead, local government is de facto run by traditional monarchs and governments organized during the war of independence.
To sum it up, the Timurid Empire is sort of a cross between traditional tribal federation and a Republican dictatorship.