I'm not terribly knowledge about the region and am figuring out a lot of this as I go, so I welcome any informed challenge on anything I say here. But my hypothesis right now is that it would be mistaken to assume that popular support for the PKK in Turkey and and the YPG in Syria are primarily based on their political ideologies. In each country, Kurds in general support whatever party or parties have been best able to deliver concrete autonomy and security over time, largely regardless of ideology.
When the PKK formed in Turkey during the 1970s, it was a Leninist national liberation movement which enjoyed Soviet support in a struggle for independence against the Turkish state. The present ideology of the PKK (and later the YPG in Syria) began to emerge much later on, in a moment of crisis in the late 1990s and early 2000s when leader Abdullah Öcalan was captured and imprisoned. It was primarily from prison that Öcalan began to propose new ideologies like "democratic confederalism" and "jineology (a kind of feminism). In formulating these ideas, he was reflecting not only on Western authors like Murray Bookchin and Immanuel Wallerstein but also on the practice that emerged of necessity int the 1990s when the PDK was basically defeated militarily and sought new ways to build mass support.
The PDK in Iraq predates the PKK by decades, and the PUK is only slightly newer than the PKK. Both started with conventional leftist-nationalist ideologies similar to that of the PKK. Their evolution over time is complex but both have built up and maintained significant bases of support over decades. Most importantly, these parties were not defeated to the extent that the PKK was. These parties became the overseers of a Kurdish region with political autonomy that the PKK never managed to deliver.
In Syria, I think the most important bit of historical background to note may be that the Kurdish population is smaller here then in the other countries. The PDKS has a similar history to the other Kurdish nationalist parties and also predates the PKK. I suspect an important part of the rise of the YPG may have to do with the relative weakness of the PDKS. The YPG is primarily a militia rather than a political party and it formed quite recently.
Now in this overall context, I think we can better understand the relative failure of the PÇDK to gain support in Iraq. It formed in 2002, when the PKK was in the process of re-inventing itself with a new ideology. That ideology seems to have been a major inspiration for PÇDK to form. But unlike the PKK, it had multiple established competitors in a position of relative strength. The YPG in Syria emerged later and adopted similar ideology, but security, not political ideology, was its primary reason for being.