Hi,

Is there a way to get the "active" (the one with solid line) connection of a node with python?
Surely I can query Switch parameter to find out which one is it, but isn't there any shortcut method?

I don't think there is
but even if it was, it would probably not be easier than node.evalParm("input")
the main reason why I think that is that the dashed/solid lines don't represent anything intrinsic (like active or not), it's up to a node to define some inputs as reference inputs (dashed line), but that doesn't really mean anything, just visual indication
so while for switch youmay be tempted to infer the activness from it, but you may run into issues where the lines are simply not updated properly until the node cooks, so it wouldnt be reliable to infer state of the node from unreliable visual indicator

so I'd go for parm value 100%

Got you.
I was just trying to cover edge case where I don't know the name of the parameter that is switching.