Before WWI the Kurdish people were split between the Ottoman Empire, Persia, and a tiny number in the Russian Empire.
The Ottomans entered WWI when a faction within it pulled an ill-advised gamer move against Russia that pushed the whole state into the war. Persia under the Qajar dynasty was very weak and informally controlled in large areas by Russia and the British so although they were officially neutral basically nobody else respected that so they were a battleground also. The Entente basically surrounded the Ottomans except for in the European part and they also had powerful naval forces so there were many fronts to the war. The British got a foothold in Iraq and convinced the Arabs to rebel. The Ottomans were losing ground gradually, especially in the south but fortunately for them the Russians fell to pieces so from there they could rest or advance on the northern Persian and Caucasus fronts and got a really good set-up there. However later on the southern fronts in Syria and Iraq were going badly and Bulgaria sued for peace which then put their now-exposed capital in Europe at risk, so the Ottoman government situated there determined the war was unwinnable and signed an unfavorable armistice that had them retreat from their gains, have some areas to be occupied by Europeans while a peace treaty was hammered out and to demobilize the army. Many of the people and army were incensed at this and would keep fighting at small scale. During this time Ataturk put out a communication that said the country’s independence and integrity was in grave danger, that the government was compromised and that delegates from the provinces should hold congresses in the safest areas of Turkey away from outside influence to determine the path forward. These established a burgeoning rival government to the one in the capital which was hemorrhaging legitimacy since it was being pressured by forces stationed right there to be compliant. As part of the new order envisioned in the newly drafted Treaty of Sevres, in addition to the ceding of land and influence to the British and French, there were also to be cessions to Greece, Italy and Armenia as well as a Kurdish autonomy or independence.
By that point though control of the unoccupied areas had firmly shifted to the Ankara government which did not agree to the terms. It warred with Armenia over their disputed territory and won, then when the Bolsheviks took over Armenia shortly after Turkey series of treaties with them that basically established the current borders and friendly relations (both had similar enemies at the time and wanted some friendly borders which would continue until Stalin fumbled things later). So that border set as Turkish one side, Soviet on the other. There was a small Kurdish population that they would intermittently make an autonomy (“Red Kurdistan”) for when sweet-talking Kurdish groups and then dissolve later, but no intention of independence from the USSR. There had been some earlier instances of Kurds revolting in Armenia and Azerbaijan but that was all squished by the time the Soviets rolled in.
Turkey continued with wars against the occupying powers and after forcing back a Greek attempt to push for Ankara the French agreed to settle the border (some modication would occur later w.r.t. Hatay state) in exchange for Turkey recognizing Syria as French in a 1921 treaty. There was a small Kurdish population in Syria at the time but more would flee there from turmoil in southeastern Turkey later. That was great as far as the French were concerned and they encouraged that since they figured that would boost the economy and simultaneously weaken the issue of Arab nationalism plaguing them in Syria (the Terrier Plan) but they wanted to control Syria themselves, not to give it to the anyone. Neither did Syria later on though under Assad rule it did allow Kurdish separatist groups aimed at Turkey to use some areas as training grounds safely out of Turkish reach so it would have leverage to make demands on other matters. Way way later on the SDF was able to control a decent chunk of Syria in the chaos of the Syrian civil war but they recently saw much of their majority Arab territories swap over to the new Syrian government and with a really bad situation if it goes to military means again they are integrating now.
The 1923 Treaty of Lausanne officially canceled the Treaty of Sevres and confirmed the border Turkey had with French Syria but the border with British Iraq was more contentious and was left tbd since both sides wanted the Mosul area (which was expected to be rich in oil). It was referred to the League of Nations which settled in favor of the area belonging to Iraq in 1926. Turkey was miffed but the British agreed to give them a part of the oil revenue and some other sweet rights and benefits so the Turks signed a treaty with them on it. The British did not want an independent Kurdistan because the oil was necessary for their navy and King Faisal of Iraq (a Sunni Arab) wanted to be able to have a higher Sunni population to balance against the many Shia Arabs in his kingdom. The Barzanis especially tried many many many times to get Kurdish state off the ground. Such attempts have been helped out at times by Turkey, Iran, the US etc. whenever they wanted to tweak the British/Iraq and presently they have an autonomous region albeit smaller than it was before the failed independence referendum.
Anyway in the meantime relations between Turks and Kurds had gone way south. For some background Sunni Kurds had for centuries been favored by the Ottoman governments and granted many traditional rights (albeit eroded in the latest Ottoman modernization campaigns) in exchange for serving as the first line of defense against the Shia leaning Qizilbash Turks who were often aligned with the various Iranian dynasties. After Turkey won back control of Thrace and Istanbul it had ended the monarchy but maintained the role of the former sultan as Caliph. The Caliph went into exile and his cousin was subsequently elected as new Caliph but it was a powerless position. He asked for more money and foreign scholars asked for him to have more power, but aggressive secularist Ataturk (who does not want religious influence entering politics) seized on this potential channel for “foreign influence” as grounds to actually abolish the Caliphate as well and force the Caliph and his family out of the country. He made many secular reforms in an attempt to shift from religious based identity to a Turkish national identity and promoted the Turkish language in line with that nation-state model.
All of that was quite toxic to Sunni traditionalists, and to ones who were also Kurdish it was viewed as sundering the only link that tied them together so that was an extra twist of the knife. Sheikh Said called all Muslims to rise up but he was only really answered by Kurdish groups (though notably some Kurdish Qizilbash who had previous been a big pain for the Ottomans opposed Sheikh Said). They laid siege to Diyarbakir but ultimately the rebellion was crushed. It was very expensive and worrisome for the Turkish government which commissioned a report on what to do. The Report for Reform in the East made many extreme recommendations on what to do that kicked Turkification into overdrive, established martial law in eastern areas and so on and made life very difficult for Kurds. In my opinion it sowed the seeds of many future problems ex. Dersim massacre. But as of yet despite insurgencies and the like, no Kurdish autonomy or independent state has been allowed from Turkey.
Qajar Iran was kind of a doormat that everyone stepped on. Much of it was basically occupied by the British and Russians and at times in WWI the Ottomans were making serious incursions. The Ottomans and early Turkey supported a revolt by Simko Shikak in western Iran (who had earlier fought them) who was eventually put down and forced into exile in Iraq by the new Pahlavi dynasty. Later on as described before Kurdish relations had gotten worse and rebellions were becoming a problem in Turkey so Turkey and Iran agreed to delimit the border more strictly which set the modern borders (very similar to older ones excluding ex. loss of Iraq) in 1937. In WWII Iran got invaded by the British and Soviets accompanied by some revolts. At the end of the war the British and the Soviets were supposed to leave but pro Soviet governments were declared in Mahabad (Kurdish) and Tabriz (Azeri). Tribes in the British occupation zone were not interested though and these attempted states collapsed when the Soviets blinked under American pressure and withdrew to leave them to Iran’s mercies. Some support flowed from the USSR and even Saddam’s Iraq to Kurdish groups in Iran (which similarly meddled back in Iraq) with a big revolt after the Iranian Revolution. Of course as you’ll know this didn’t work though some Kurdish insurgent groups exist to this day.
To make a long story short, the folks altering the maps were generally looking to do so in their own favor. Kurdish independence was mostly something to support somewhere else that you didn’t plan on annexing yourself and that would cause a power you were concerned with to be distracted. These were largely very poor tribal areas so with a poor economy they don’t have much ‘oomph’ so to speak in a prolonged war themselves so they would need support… which is also hard to provide because as they’re landlocked a ways in from the water you need the backing of a neighbor to actually get arms and supplies to them. And all the countries currently with a large Kurdish population - Iran, Iraq, Syria, Turkey - share an incentive to not actually want an independent Kurdish state that would may be ideologically inclined to provide a safe haven for their separatists to retreat to and strike back from. Plus Kurdish people are ideologically divided with constellations of parties with different objectives.
I’m flattered but I don’t know the first thing about modding and I’m just here to goof off so I don’t want to make it a chore, if that makes sense. I’ll certainly subscribe to that group, though.