Either during or in the immediate aftermath of World War II,
the Soviet Union decides to press its territorial claims against Turkey and invades the country. The Turks are crushed, and as part of the settlement, Istanbul is directly annexed by the USSR (Turkish Thrace is granted to Bulgaria).
The Soviet Union collapses at some point down the line, but rather than staying with Russia or being retaken by Turkey, Istanbul/Constantinople, with its complex ethnic mix of Greeks, Slavs, Turks, and others, defaults into independent city-state status.