Back then, the Crimea and surrounding areas of Ukraine were part of the Crimean Khanate, an Ottoman vassal ruled by the Giray dynasty who are descendants of Genghis Khan. While technically independent, their prestige and influence has been severely curbed from the 17th century due to the increasing Ottoman control.

The khanate was separated from Ottoman hands after the Russo-Turkish War of 1768-1774. It started when after the death of Polish King Augustus III, Polish Catholic nobles rebelled against the new king, who was Orthodox and backed by Russia, and appealed to Ottoman Mustafa III for help. The Porte has been keeping an eye on Russia for a while as their expansion throws the balance of power in the Northern Frontier to Russian hands, and so when a Russian army chasing down the retreating Polish and Cossack rebels entered and violated Ottoman territory the Porte declared war. The Ottoman Empire were woefully unprepared for war, and not only the army quality had much deteriorated after a long peace, the usually excellent Ottoman supply network also broke down because of neglect and lack of action. Despite fierce resistance against the Russian force like in Hotin, the Ottoman army can't defeat the Russian army who were not only forged by the Seven Years Wars but also is under capable leadership. By 1770, exhausted, the two sides called a truce and tried to make peace but Russian demands were viewed too extreme and hostilities continued. The Ottomans continued their resistance and even though they held their ground, they could not maintain their strength indefinitely and the main Ottoman army was surrounded at its headquarters at Sumnu so they sued for peace

The treaty concluded that the Ottomans must grant the Crimean Khanate independence under Russian protection, amongst other things. The Ottomans couldn't cope with this loss and sent a troops and fleet to support a revolt led by Ottoman loyalist Devlet Giray against the Russophile Khan Shahin Giray installed by Catherine. After they were repulsed by the Russians, Catherine then annexed the Crimean Khanate cited the inability of the khanate’s inhabitants since independence to enjoy the fruits of their freedom as a cause

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Sources:

Ottoman Wars 1700-1870 by Virginia Aksan

The Russo-Turkish War, 1768-1774 by Brian Davies