In the timeline, Constantinople never fell to the Ottomans, and became an independent city-state, and later nation-state.
In the ATL, the Black Death never reached the city, and a different, less expierenced Ottoman general invaded. Although the city was damaged, the local government (in the absence of the dead Byzantine monarch) negotiated a peace treaty. Constantinople would run its own affairs without fear of further Ottoman military aggravation, but the new country would allow the empire open borders. The Byzantine empire collapsed only days later, leaving the economic powerhouse of the Kingdom of Constantinople in its wake.
Constantinople expanded in to the former Balkans in the coming centuries, staying along the OTL Greek coast, and claiming some of the islands once left lawless by the fall of the Byzantines.
Because of Constantinople's status as a basic satellite state of the Ottoman Empire, the country fought on the side of the Ottomans in every conflict they participated in, from the Conquest of Cyprus to World War One.
With the help of Constantinople and many of the former Central Powers, the Turkish War of Independence was defeated, and the Ottomans survived for many more years until 1939, when World War II began. The empire balkanized after 650 years of strain, and Constantinople, now and independent and free nation, expanded its borders into the lawless regions of OTL Turkey, Georgia, and Armenia.
Following World War III in 1962, Constantinople reformed the United Nations in the capital city, becoming a centerpiece of world politics.
By 2000, Constantinople had become an influential nation in Europe, being the heart of Eurozone development, a hotspot for European football having hosted the UEFA Championship five times, and a symbol of national struggle.