I'll try to answer your question, sorry if it doesn't satisfy you

The relations between the Ottomans and the Kurds started after the battle of Çaldıran in 1514, where many of the Shafi'i Kurds joined the Ottomans against the Shi'a Safavids. After the negotiations between Ottoman envoy and Kurdish emirs, the Kurdish emirs decided to declare their allegiance to the Ottoman sultan. The Kurds were obligated to provide soldiers and military supplies to the central government when the Ottomans entered any war, in exchange they were given various economic and political privileges, including fiscal, judicial and administrative autonomy over their region and the privilege of keeping their hereditary property and principalities. To govern the disparate Kurdish tribes, Ottoman administration in Kurdistan varied greatly. The degree of autonomy granted to the Kurdish emirates was based primarily upon the accessibility of the land, the importance of said land, and the strength of a Kurdish tribe. The least powerful tribes were either forced to join more powerful ones or to become a part of the regular Ottoman sancak. The most powerful and least accessible tribes enjoyed the highest degree of autonomy. So generally, in the 16th century, the Ottomans secured Kurdish loyalty by sacrificing local autonomy, and the Ottomans interfered in local politics only when tribal feuding threatened the security of the empire’s borders or the trade routes that passed through the mountains of Kurdistan. Of course this autonomy experienced an ebb and flow, for example in the 17th century there's a considerable attempt by the Porte to reduce the autonomy of Kurdish tribes and emirates, and while in the end they still retained their holdings and property, the Kurds becomes increasingly compliant to Ottoman demands. This relations would broke down by the Tanzimat, due to the centralization policy adopted by the Porte. This led to significant restrictions on Kurdish autonomy which led to revolts of the Kurdish emirates in the 1840s, notably the ones led by the Emirate of Botan. Though the Ottomans defeated these revolts, destroyed the emirates and centralized their rule in the region, it was evident that they couldn't hold the region effectively, due to oppositions from Kurdish tribes. Because of that, during the Hamidian Period, Kurdish tribal sections were organized by the Hamidiye Cavalry. The Hamidiye were an irregular cavalry and proxy force in eastern Anatolia created by Sultan Abdülhamid II from selected Sunni Kurdish tribes to provide a bulwark against the Russians and to incorporate the Sunni Muslim Kurds into the Ottoman state system. This system successfully won Kurdish loyalty, but it exacerbates the socio-political tensions between Kurds and Armenians in the region, the latter subject to brutal massacres by the Hamidiye after a tax revolt of Armenian peasants in the Sasun region. After the CUP took power in 1908, they abolished the Hamidiye and returned Kurdistan to a centralized rule, where it had a real administrative and military presence and was also able to co-opt local elites. Kurdish intellectuals during this time generally hosted a weak Kurdish nationalist movement, but a strong Islamic identity and powerful loyalties to the idea of Ottomanism with regards of autonomy for Kurdistan, which was cultivated during the Hamidian era. I can write on more detail about Ottoman administration of Kurdistan, but i think it would miss the main point of your question, and this is just a kind of preface on how the Ottoman government overall view the Kurds and Kurdistan.

So about the meat of your question, the answer is complicated. First things first, Kurds did indeed faced a degree of prejudice and discrimination, but this was mainly targeted towards tribal nomadic Kurds, which has the tendency of raiding and pillaging villages. Urban and sedentary Kurds were generally accepted and viewed as equals, considering there were many Kurdish notables, intellectuals, and urbanites living in cities like Damascus and Istanbul and attained high positions there (Gökalp once famously asserted that şehrî'nin milliyeti yoktur, the city dweller has no nationality), but these Kurds were not labeled as Kurds, and those who were labeled Kurds were tribal, volatile ones. To sum it up, no city or village resident was formally labeled “Turk” or “Kurd,” although the tribal past of settled Turkomans or Kurds was often remembered as a nickname, like “that little Turkmen” or “Kurd So-and-so.” Rather, ethnicity was a marker of nonsedentary cultures, a label of “nonresidency” and therefore, in the eyes of the “resident,” of the absence of the civilizational attributes of the sedentary.

But people are prone to generalization and racial stereotyping, so these urban Kurds still sometimes faced discrimination and prejudice on the grounds that they are Kurds, and therefore the same as the tribal Kurds. There were many examples of Ottoman notables looking down on Kurds because of the tribal stereotypes. For example when in Diyarbekir, Evliya Çelebi depicted Kurds as "primitive, treacherous, quarrelsome and bloodthirsty", but he only gave this "Kurd" label to tribal, nomadic Kurds. The fief-holders, tax-collectors, craftsmen, and merchants who resided in the town are not given any specific racial label, despite them being predominantly Kurds or Kurdish-speakers. Mustafa Ali also called the Kurds as "perfidious, whose character is nothing but obstinacy and stubbornness" but he used it in conjunction with the Turkomans, who were also nomadic groups who frequently raided villages. This also bled to local population, whose fear of tribal Kurds gave them prejudice towards sedentary Kurds. For example in the city of Ayntab, a certain Yunis protested the marriage his mother had made for his sister Fatma because her fiancee was Kurdish. He stated in court that “there is no social equivalence, the fiancee is of Kurdish origin and my sister is the daughter of a scholarly family” This incident is an example of antagonism between urban elites and those deemed lacking in urban sophistication because of their tribal backgrounds. On the brighter side, in the same city there was a community protest against the unjustified imprisonment of a certain Kurd named Seyfeddin. So generally urban Kurds were accepted, though there were prejudices and racial stereotyping like i described above.

Tribal Kurds was still viewed as a menace up to the 19th century, For example during the establishment of the Hamidiye Cavalry, Muslim notables in Erzurum regarded the Kurds as a “bloodthirsty, savage population, which is used to plundering and nomadic life”, which would “never submit to discipline straight off” and that they had “no attachment to the Ottoman government” and that they did not even “identify with the Empire”. Abdülhamid II also referred tribal Kurds as "savages" and "uncivilized", but again this was mostly because of their tribal organization and their tendency to raiding and banditry, using freedom as license.

Sources:

Disliking Others: Loathing, Hostility, and Distrust in Pre-Modern Ottoman Lands edited by Hakan T. Karateke, H. Erdem Çıpa, and Helga Anetshofer

Kurdish Notables and the Ottoman State: Evolving Identities, Competing Loyalties, and Shifting Boundaries by Hakan Özoglu

Morality Tales: Law and Gender in the Ottoman Court of Ayntab by Leslie Pierce

Ruling the Periphery, Governing the Land: The Making of the Modern Ottoman State in Kurdistan, 1840–70 by Nilay Özok-Gündogan

The Margins of Empire: Kurdish Militias in the Ottoman Tribal Zone by Janet Klein

The Ottomanism of the Non-Turkish Groups: The Arabs and the Kurds after 1908 by Hamit Bozarslan

The State and Kurds in Turkey: The Question of Assimilation by Metin Heper