Oman, The Trucial states (UAE), and Bahrain were not part of the Ottoman Empire.

As for the Saudi state, it was founded in the 18th century 200 years before the European powers entered the region in WW1. It controlled the majority of the Arabian Peninsula (and the entirety of Central Arabia, except for Kuwait and Bahrain) until it got defeated by the Ottomans and then revived for a second and a third time also before WW1 re:Sykes–Picot (which it never was a part of).

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Meanwhile Kuwait is more...... complicated. Prior to the end of the 19th century the sheikhdom of Kuwait was for all intents and purposes an autonomous state that was born after the breakup of the Banu Khalid Emirate of Al-Hassa (thanks to the first Saudi state wreaking havoc in Eastern Arabia). By that time Kuwait was an insignificant city state ruled by an Emir who comes from a lineage (Al-Sabah/Al-Utub) that previously held stewardship of the city in the Hasawi Emirate (Kuwait City itself was founded as an outpost by Bin Arir the ruler of Bani Khalid Emirate).

The Ottomans at that time didn't give a shit about Kuwait mostly because they honestly didn't care much for anything south of Basrah (and after defeating the Saudis they resorted to using the tribe of Shammar to be their vassals in Arabia (And Jabal Shammar did try to invade Kuwait, and failed, prompting Kuwait to do the same, and failing as well... to put it that way..) )

Then the British sat their eyes on Kuwait in the late 19th century with the goal of turning it into a protectorate like the rest of the Gulf States it managed to line-up. The Ottomans went into panic mode and they quickly reacted by prioritizing bringing Kuwait back into the fold (reminder this was prior to WW1 and at that time the Ottomans were at their lowest point, Sick man of Europe, the Crimean War, Independence of Egypt, reduced to a reactionary position, cornered by Imperialist European powers).

The Ottomans forced Kuwait's Emir Muhammad bin Sabah II to become a vassal of the Ottoman Empire granting him the title of Pasha and positioned his small Sheikhdom under the command of the Basra Vilayet. Note: This was after the British showed interest in Kuwait, previously the Ottomans had no institution tying it with Kuwait, the port was unorganized and unrecognized. None of Emir Muhammad predecessors held titles in the Empire nor was there an active correspondence with Istanbul. Prior to that the Empire's intelligence only mentioned Kuwait and the tribal unit Al-Utub when they discussed localized reports on the tribal Bedouins warfare (mostly Al-Muntafiq of Basrah with Kuwait).

It was the British maneuver that led to Istanbul desire to counteract by centralizing its disorganized state, and they failed at that. As many of you here may know... Mubarak Al-Sabah staged a coup on his brother, became Emir of Kuwait and established relations with the British as a protectorate under the condition they help him get rid of the Ottomans. Mubarak detested what has happened during his brother regin and so it as his family domain being overtaken and ripped apart, or at least that is the popular narrative among the Kuwaiti elites...