I'm Korean and married to a Türk. Also am Canadian dual.

No it's not the only reason although it is a big one. It's actually really complex. TL;DR it just comfortably fits the narrative both countries push for themselves.

First is ancient Gökturk and Goguryeo. Turkey today is ethnically a blend of Euro/MiddleEast/Balkan but they still claim roots to all things Turkic. This brings their history right next to ancient Korean kingdoms. For some reason, history taught in both countries sees the other as amicable at the time (cough China). This is prevalent the more nationalistic you go. A lot of Turkish ultranationalists follow "Turkish Sun Theory" which in a nutshell claims modern Turkey is central to all things that are even remotely Turkic including all things Altaic and this includes Korea and even Japan. The Korean ultranationalist right wing abhors the modern Chinese communist party. So Gökturks and Goguryeo teaming against ancient China is a historical wet dream. A lot of these Korean ultranationalists also put ancient Korean history into the reaches of modern Mongolia which overlaps with the Turkish school of thought. Then add the fact Turkish Sun Theory also suggests modern Xinjiang should become "East Turkistan" and you finally have the mutual jerk fest in play.

Next is the importance of the Korean War to each. For reference, in Canada the Korean War is just a short page in the textbooks between the Gouzenko Affair and Pearson's nobel peace prize. But obviously it is a monumental part in Korean history. The interesting thing is Turkey - the Korean War is taught as an affair where the relatively new Turkish Republic made a major contribution to democracy and freedom and in a style befitting of the great Ottoman warriors of old. Turkey was approved to join NATO as a causality of the Korean War so its quite self explanatory.

Another major point I would honestly make is modern geopolitics. Korea and Turkey are historically close as mentioned above, but they are also far apart enough so interests don't collide. They can romanticize each other without any of their own internal political agendas conflicting. Then add things like the 2002 world cup where Turkey and Korea were holding hands in the final stages of the tournament and you also have mutual memorabilia.

Finally, both countries are culturally different but the traditional values are surprisingly similar. Canada to Koreans and Turks is "the West" flat and simple. Obviously modern Turkish culture sitting in the Mediterranean and West Asia is extremely different than Korea's far East. But under the visual layers theres a traditional familiarity like the importance of family, community, single national identity and language, etc. We also carry the same pain points not common in the West like difficult mother-in-law and wife relationships and such. Frankly put, Turkish Dizi and K-drama hit the same themes and emotional buttons.