Please consider this: if war does break out between two NATO members, Greece and Turkey, what does NATO do? Bonus question: How long can Turkey remain in NATO?
I don’t think you’d ever come to full-up war on Turkey-Greece. It’d some stupid episode where a Turkish junior captain on a vessel fires on some fishing vessels, and some brief ten to twenty day conflict would exist on paper (in the fake sense).
The US would pretend that nothing never really escalated. The French and British would mostly want to talk. Germany might want to send three vessels down for Greece but two will be broke down for six weeks, awaiting parts, and the third which does deploy...has a Turk-German captain in charge of the vessel, with a Greek-German as number two.
Putin would eventually get involved and suggest that he’ll set up a no-fly zone over the region and shoot down any Turkish aircraft. After that....things will cool off real quick, and the whole incident will be forgotten in six months.