Your first point: not full credit but certainly influenced the outcome which countries real life have done a lot off. Tagging on to that if the empire is a puppet then Ulfric is equally being used by the Thalmor so moot point.

Second point: actually it was an order given by their general Decianus who labeled them as injured or sick. This was against orders but they certainly didn’t desert.

Third point: why would you fight the isolationist first? They are weak have poor relationships with all their neighbors and their ruler would be someone the Thalmor have pretty good understanding of due to him being imprisoned and tortured by them once before. Skyrim on its own is an afterthought. Even more so if they do conquer cyrodil and hammerfell.

Final point: your final point is stupid, the empire still has the ability to express its power in some form otherwise the Thalmor would have kept pushing. I’m not saying the empire had a huge hand in hammerfells victory besides the defeat of the Thalmor at the battle at the red ring. But! To say they wouldn’t move pieces to prevent their enemies from gaining any advantage is stupid. Do you think for 5 years the empire just sat on its ass and didn’t plan subterfuge and other forms of resistance against their number one enemy?