Dont forget that after that Turkey ended up in NATO. Zones of Russian and Turkish 'natural' spheres of influence cross each other and that is the main reason of their tensions, no matter what political party rules over these countries.The Iranians would be involved in any case in the war against Israel. Maybe not by sending large amounts of their military, but pushing their proxies in Lebanon and Syria.However. . . if Israel used it's superior tech, even limited, like a tactical nuke on a major Turkish military or civilian target. . . that would really risk bringing in either the Russians or the Iranians
About the Russians.. It is doubtful they would get involved on Turkey's side. After all, Turkey and Russia have been adversaries throughout virtually all of their history and Russia isnt too interested in Turkey becoming regional super power.
Conflict was between Tsarist Russia and Ottoman Empire.
Bolshevik Russia just like the Muslims of Indian subcontinent supported Turkey during fall of Ottoman Empire.
Without material help from Lenin Atatürk couldn't succeed founding Turkey and Turkey would be just another country whose borders where drawn by imperialist designs.
In Momument of the Republic (Republic Monument - Wikipedia) both Frunze and Voroshilov are portrayed besides Atatürk.
In those "spheres of influences" there are still countries exerting influence which are alien to this region.
In Caucasus it was Minsk Group (USA, France), in Libya it was France.
Now Russia and Turkey call the shots there with the imperialists reduced to issuing statements.
There's enough room in the region for both Russia and Turkey to advance its interests, at the expense of others, off course.