It's was never about oil. Do a little research on the massacres history of Northern Iraq(I mean not KRG but north of country) cities from Musul to Kerkük.
Also, the oil resources you mentioned are already shared between western oil companies.
Between 1999 and 2004 there was a ceasefire – I am ashamed to say. In other words, there was no cross-border operation.
Then, in 2005 the most serious mistake of the AKP, the solution process nonsense, started. (It was formalized by law in 2009)
In short, what you said is a completely unsupported and unaware interpretation from actual historical events.
After the Ceylanpınar massacre in 2015, the 'Solution Process' de facto ended and it was decided to completely destroy the PKK terrorist organization as it did not lay down its arms. After Turkey started this struggle, many countries, especially the USA, are trying to protect the PKK officially.
And there was never an operation plan for Kirkuk.
Let alone Kirkuk, even when the Turkmen city of Talafer was devastated by terrorist massacres, we were devastated here and could not make the government take a step.