I think folding the turn is likely fine, weak top pair OOP with so many horrible river cards that it's very hard for us to win the hand. The flop is the bit that I'm really unsure of the plan and how we want to play this hand but I probably play pretty horribly on monotone boards like this.
On the flop villain has more strong and nutted flushes and Adx in our range than we do (as we 3bet some), all sets (we 3bet KK), similar amounts of two pair, better Kx hands (we 3bet strong Kings).
Maybe due to odds pre we have a lot more flushes in our range than villain does? But on average weaker flushes but as we are stacks are so low I think having more flushes even if they are on average weaker is better for us.
In reality I probably call the turn and fold far too much on the river but I'm pretty lost in this spot. I think holding a diamond kicker is better for us especially when most of the weaker kickers in villains Kx made two pair.