If you declare a Winged Guardian as a defender, and then use Swift Strike to kill the attacker, does the attack "resolve", in which case you have to pay a resource to keep the Winged Guardian in play?

Or does an attack only "resolve" if its shadow card is flipped?

The attack does not resolve because the attacker in no longer in play to attack. Your Winged Guardian is not discarded.

I feel like Swift Strike is a bit underrated in the current meta. 2 tactics resources is not as expensive as it used to be.

True, but two damage isn't as expensive either.