NL20 Top set river bluff jam on 4 suited card board?

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NL20 Top set river bluff jam on 4 suited card board?

Blinds: $0.10/$0.20 (6 Players) BB: $39.17
UTG: $35.55
MP: $20.00
CO: $17.35
BN: $25.59 (Hero)
SB: $56.62
Preflop ($0.30) Hero is BN with K K
3 folds, Hero raises to $0.60, SB folds, BB calls $0.40
Flop ($1.30) 5 4 K
BB checks, Hero bets $0.65, BB raises to $1.62, Hero raises to $4.31, BB calls $2.69
Turn ($9.92) 5 4 K Q
BB bets $6.94, Hero calls $6.94
River ($23.80) 5 4 K Q 2
BB checks, Hero checks
Final Pot UTG wins $0.00 CO wins $0.00 BB wins $22.61 MP wins $0.00 SB wins $0.00 BN wins $0.00
Rake is $1.19

First on the turn I almost feel like exploitatively folding here (and just calling with the nut flush although I don't know if I would ever 3-bet the flop with the nut flush draw) as I feel villain has essentially no bluffs but we only need 29% equity and we have 23% vs any flush so considering possible implied odds I guess we call.

I feel villain will almost always jam river with their nut flushes in order not to let sets go to show down, although maybe very occasionally villain might trap. So I feel villain is very likely to have a low to mid flush here.

So my question is can we jam river to try and rep the nut flush out story makes sense as we can sometimes have AA with spade and we mostly call any Axss nut flushes to trap on turn. But do we generate enough folds to justify a jam?

Pretty interesting spot I think although maybe I'm overthinking and it's a clear jam as we almost never win at showndown.

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