Not quite.
Ottoman empire circa 1914
Turkey may want to grab Syria, but the Iranians won't allow that
The Turks also may want to take Armenia, but more likely just keep it as a vassal state (it provides them no benefits).
Any adventures into Greece or Cyprus would bring it into other countries' spheres of interest.
Furthermore, look at Turkiye's economy under Erdogan
and inflation
Turkey MAY want to get the Caucasian lands, but can they?
“Turkey MAY want to get the Caucasian lands, but can they?”
More likely they would exercise soft power to support independence of Turkic peoples from Russia (and closer to Turkey). Political and diplomatic support in International relations; covert support and agitation.
Although the Turkish economy is a basket case, they have one of the top ten defense industrial bases on Earth (Turkish companies got the contract to expand US artillery shell production in Texas). Turkey also exercises a lot of soft power and influence in Muslim Central Asia, with popular media (TV, movies, music), as well as religious and cultural outreach programs.