Transmission Question

[vcmt]

My 300SEL transmission cooling hose broke the other day car just stopped. Replaced it and the car runs perfect . Before the car would have trouble idling In park neturel or drive I figured i had a vacum leak I spent a lot of time looking for it.

So my question what fixed the idling problem?
Does the transmission work off vacum and adding fluid to the correct level
somehow fixed it ?

Or maybe low fluid level put stress on the engine affecting the idle ?

Whats the relationship between transmission and idling?

Thanks in advance
Tim