Don't lead into the preflop raiser on dry boards, but when you bink the straight on the river, check to let them bluff their missed draws.
Leading into the preflop raiser (donking) on a King-high dry board is a significant error. We should check our entire range here to protect our strategy.
Note: Donk betting here is a mistake; this board heavily favors the CO's range, and we should check to realize our equity with an open-ended straight draw.
After our flop lead is called, checking the turn is the standard play to control the pot size now that we've improved to second pair.
Calling the turn bet is mandatory. We have second pair and an open-ended straight draw, giving us plenty of equity to continue against a wide CO range.
We hit the straight, but checking is the highest EV play. Since we led the flop, Villain expects us to continue betting our strongest hands; checking induces bluffs.