Will Syria become a Russian state now that the war is almost over because the West certainly didn't win?

Russia supported Syria before, they will continue to bring it back to it's previous level. As well as help clear out the terrorist forces.

Did the west actually want it?? Impoverished, war torn, destroyed countries with shell shocked people would be a feather in the west's cap would it??

the west didn't win what ?

More likely it will become a branch of Iran.

Highly unlikely. Syria does not border Russia nor do any of Syria's neighbors want a Russian state. The United Nations would condemn any such actions (a big "so what" to Russia) and NATO might have an interest in that not happening as well.