I'll try to answer your question, sorry if it doesn't satisfy you. I'll be focusing on the Ottoman Empire. The Ottomans were a particularly active player in the attempt to preserve Polish independence, so this will be quite long

For starters, the Ottoman Empire and its nominal vassal the Crimean Khanate were VERY concerned with the independence of Poland. Contrary to what some would tell you, the Ottomans and Poland enjoyed a mostly friendly (but rocky) relationships until the 17th century. Even the treaty of Karlowitz did not severely damage relations between the two states and was designed to preserve 'lasting peace' between the Ottomans and Poland. After the treaty of Karlowitz, the Ottomans tried to preserve what was seen as the 'balance of power' in Eastern Europe and to prevent the rise of Russia, which is why they supported the Swedes in the Northern Wars and tried their best to stay neutral in the conflicts of 18th century. On that agenda is also to preserve Poland as a strong, nominally friendly state to bulk against Russian threat. Early attempts to protect Polish sovereignty can be seen at the Treaty of Pruth (1711) which prevented Russia from intervening in the internal affairs of Poland and its royal elections. This was continued in the Polish Succession Crisis when Stainslaw Poniatowski, one of the pro-Ottoman figures in Poland messaged the Grand Vizier Seyyid Mehmed Pasha to ask to prevent the accession of the pro-Russian August III by landing troops in Poland and upheld the Treaty of Pruth. However when the Polish War of Succession (1733-1738) broke out, the Ottomans opted to stay neutral because of their ongoing Persian campaign. They did protested though, with Seyyid Mehmed Pasha sending a letter to the Hetman of Poland stating how Russian involvement has violated the Treaty of Karlowitz and asserted that Poland was under Ottoman protection. Eventually the Ottomans did dragged into War with Austria and Russia, though it was partially initiated by Crimean Khan Kaplan Giray who were anxious to prevent Russian expansion.

Things started to get heated again in the late 1760s, with the growing anti-Russian sentiment in Poland. The Ottomans were initially passive when August Poniatowski, another pro-Russian Polish king were once again elected, with the Ottomans only sending another protest and warning. Increasing diplomatic tensions between Russia and the Ottomans coincided with the emergence of anti-Russian sentiment in Poland, and these insurgents did not hide their hope for intervention from the Ottoman Empire and Crimea. This resulted in a rebellion and creation of Bar Confederation, who asked for Crimean assistance. Khan Maqsud Giray hesitated, especially when the Porte was divided by factional strife. The Ottoman Empire eventually declared war to Russia in October 1768 after the Cossacks attacked the city of Balta. The declaration of war issued by the Porte clearly stated the events in Poland, Bar Confederation and also the Balta incident were the causes of war, with one of the demands being the withdrawal of Russian troops in Poland. The Russians played out a delaying tactic, and announced that it would carry out the "Polish Expedition" in 1769

The war infamously went really bad for the Ottomans, with their army incapacitated thanks to poor logistics and organization. Things went bad to worse when Austria who initially supported the Ottomans annulled their agreement when Austria concluded a treaty with Russia and Prussia in 1772 for the division of Poland. In the end, the Russo-Turkish War of 1768 resulted in the destruction of Bar Confederation, Partition of Poland, territorial losses, and the miserable independence, later annexation of the Crimean Khanate. This effectively ended chances for further Ottoman intervention in Poland. More attempts for additional Ottoman support were requested by some Polish noblemen in the 1780s, but it ended nowhere. The outbreak of Russo-Turkish War in 1787 gave a respite for Poland, who enacted reforms under the so-called "Four-Year Sejm" era. This also once again opened negotiations between Poland and the Ottomans for an alliance in 1790, which were abruptly terminated with the Treaty of Jassy (1792), which cemented Russian victory over the Ottomans and Russian troops were released to invade and subdue Poland-Lithuania one more time.

Sources:

"I. Mahmud Döneminde Osmanlı Devleti’nin Kuzey Politikasında Lehistan Faktörü" by Hacer Topaktaş

Ottoman Wars 1700-1870: An Empire Besieged by Virgina Aksan

"Realpolitik and Rhetoric in Ottoman-Polish Relations" by Hacer Topaktaş

The Crimean Khanate and Poland-Lithuania, International Diplomacy on the European Periphery by Dariusz Kołodziejczyk

The Treaties of Carlowitz (1699), Antecedents, Course and Consequences edited by Colin Heywood and Ivan Parvev