The Syrian regime and the Kurdish paramilitaries have managed to avoid the high levels of conflict seen elsewhere in the country. Over the years, there have also been reports of cooperation between Kurdish militia, militias loyal to the Syrian regime, as well as the Russian air force.
The Syrian regime viewpoint may well be that Kurdish territorial ambitions, beyond federal autonomy, will always be denied by Ankara – by military means as necessary. This has meant that the Syrian government can focus its attentions elsewhere; at least for the time being.
Recent reports show however that the Kurds have been advancing on Al-Raqqa. They are still some distance away, although they are moving in the right direction. At the moment however, the Kurds are still operating in their own ballpark, but the farther down the Euphrates they get, the more into unfamiliar Arab/sunni territory they will stray. The Kurds may well begin to ask themselves what they are doing, so far away from their homeland. Particularly since the Assad government is busy building up an attack posture of its own against Al-Raqqa.
The end of the civil war will eventually come, and the Kurdish decision-makers know that short of a collapse of Turkish statehood, the most optimal political outcome they can hope for is federal autonomy. The strength of this autonomy this will be determined by the final reckoning on the battlefield – as it was for them in Iraq. Federal autonomy can then be used to continue to build support for statehood through international mechanisms. The Kurds have come a long way towards their objective in the last twenty years, and this will be another milestone on their journey.
It is also still clear that Washington is pushing to minimize the role of Assad in post-conflict Syria, the Kurds can help, and they know this. Pushing towards Al-Raqqa will satisfy the U.S./western desire to deny Assad extensive gains against ISIS, and thus weaken his position as the different factions move towards end-game in major hostilities. With the regime now pushing ISIS and the collection of other anti-Assad forces onto the back foot however, an over-extended Kurdish position is coming into Syrian regime focus again.
The Syrians and Russians have not had to test the resolve of the U.S. led coalition to defend its Kurdish allies from a consolidated Syrian regime attack, now that U.S-forces are embedded with the Kurds. Even if they won’t retaliate to a Turkish one, it is still a risk. It still seems as though the Syrian Regime would still rather accept some form of Kurdish federalism, rather than do so. At the same time it seems that the media is now being used to weaken the Kurdish resolve to support the U.S.-coalition, at a political and international level. A standpoint questioning the reliability of U.S-led intentions towards the Kurds appears to be the messaging approach used. The example I have seen can be read here: https://www.rt.com/op-edge/345411-kurds-isis-syria-us/.
The Kurds will be acutely sensitive to their position even if they are unlikely to be swayed by the media. They have to play a balancing act: ensure that they maintain the leverage they need for negotiations, satisfy the U.S.-coalition demands – necessary for post-war political support – and avoid escalating the conflict with the Syrian and Turkish governments. At the time of writing, the visible side of this balancing act will be seen in how far they advance down the river towards Al-Raqqa.