You missed one major player in Syria...
RUSSIA
Russia is a pathetic thugocracy both internally and externally. It is no longer a ‘major player’ in Syria because its resources have been expended in Ukraine. It no longer has the funds, personnel or weapons systems to ‘play’ in Syria by the very rules it established and cultivated for the past 60 years. Assad is the thug he is due to 60 years of KGB patronage, funding, training and tutelage.
The US otoh has the assets to both set the rules and moderate activity in Syria. Example: the elimination of ISIS via thousands of drone strikes since 2014. Now Iran ‘plays’ the terrorist role on Assad’s behalf. So the four Iranians who launched the drone are now dead. Balance and peace are restored. That’s what the US is “doing” in Syria.