I'll try my best to answer this, though maybe it won't fully answer your question.

The first attempt to build a sailing vessel goes back during the reign of Mehmed II, Where he ordered to build a galleon imitating the Venetians, Aragonese an which sank during launch due to the lack of technological know-how. In the 16th century, The Ottomans build vessels similar to caravels, but isn't widespread and later abandoned because of their impracticability in the absence of wind. They did created hybrid vessels containing both oars and sails though, such as kalite, göke and burton which was widespread and frequently used to protect convoys, as transporters or corsairs and cruising against enemy ships.

Starting in 1644, The Ottomans started to realized Galleon's advantage over galleys during the campaign of Crete. In the meeting chaired by Grand Vizier Koca Mehmet Pasha they discussed how their galleys had difficulty standing up against Venetian galleons aided by wind. They immediately planned to build a sailing warship, and aided by North African and Italian shipbuilders, they launched it on 1682. The Ottomans then systematically build galleons and sailing ships onwards. The number of galleys fell to 15 in 1701 and is steadily decreasing over the century, as in 1787 there are only 6 galleys in the Ottoman navy

Their reluctance on using sailing ships also were not without reason either, since they knew the Barbary pirates in Algeria effectively used both sailing and oared ships since the mid-16th century. There are several factors causing this.

First, The prolonged rivalry with Venice. Venice was a major naval and commercial rival sharing the same geographical market with the Ottomans. Operating in the same geography compelled them to observe each other closely and to seek ways to have a greater share of the benefits of the competition. It was also the cause of their technological similarities. Long wars, commercial and technological exchanges, being obliged to cope with the difficulties of the same geography made them similar in many respects. It was difficult for either to change its well-rooted galley tradition, regardless of the possible negative outcomes, as doing so might have put it into a disadvantaged position in the face of its rival. In addition, adopting new technology meant new expenses, know-how and expertise. All these factors caused them to cling to the traditional vessels, which is more practical within the geography in question. This prudent attitude continued until this relatively peaceful geography was disturbed by the naval forces of the Atlantic powers in the 17th century.

Second, the geography in which the Ottoman navy operated. The seas of Marmara, Aegean, Mediteranean, Black and Red Sea, all made the galley often times more advantageous than galleons, as war galleys rather than galleons remained the most suitable vessels to wage naval wars and to gain possession of the bases and islands that would lead their masters to control the sea routes. They were also powered by oars, which freed them from dependence on fair wind on calm days and is able to operate close to the shore and were not visible from a great distance, thanks to their low structure in the freeboard and shallow draught. This is imposrtant because Ottoman navy crews often worked as pirates as well, especially in their affair in the Indian Ocean.

Third, is the practicality of galleys in naval warfare. During sea battles, the Ottomans were skilled at the time-tested techniques of ramming and boarding, for which galleys were well suited. Therefore, it was difficult for the Ottomans to give up these vessels for new ones, which would require a whole new way of manoeuvring in battle. Above all, galleys were amphibious forces, using their ordnance against targets ashore, covering landings and debarkations, re-supplying missions and functioning as siege batteries against coastal fortresses. Heavy ordnance was used effectively from the bows of galleys before it was from the broadsides of sailing ships. Large cannons could be accommodated on the earliest main centreline mounts on war galleys. Being simple in construction, these mounts did not require any major modification of the galley’s hull. The addition of bow artillery later on made war galleys even better suited than before for amphibious raids and skirmishing. The Mediterranean rulers of the 16th century were not faced with the choice between the war galley and sailing ship, but with how to get the most out of a limited quantity of good artillery.