While we have a strong draw and bottom pair, the monotone board and paired turn require a more defensive approach to protect our range and realize equity.
Checking is the preferred play here. While we have bottom pair and an open-ended straight draw, the monotone texture is extremely coordinated and favors the caller's range which contains many flushes and high spade draws.
Note: Betting into a monotone board with bottom pair and no spade is risky; checking allows us to realize equity and protect our checking range.
The board pairing the 6 is a neutral card, but we should still be checking. Our hand has improved to two pair, but it remains vulnerable to the existing flushes and straights.
Note: Betting here bloats the pot with a hand that is now a bluff-catcher against the most significant parts of Villain's continuing range.
Shoving the river is a massive overplay. We have a bluff-catcher that loses to all flushes, straights, and trips; by shoving, we only get called by hands that have us crushed.
Note: Turning two pair into a bluff here is unnecessary and low EV; we don't block the primary value hands like flushes or straights.