$5 NLHE 6-max: Rivering the nut flush in a 4bet pot

poker stars $0.02/$0.05 No Limit Hold'em - 6 players
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Hero (BTN): $6.03
SB: $6.11
BB: $5.22
UTG: $5.58
MP: $5.50
CO: $5.23

Pre Flop: ($0.07) Hero is BTN with A:spade: K:spade:
3 folds, Hero raises to $0.12, SB raises to $0.41, 1 fold, Hero raises to $0.90, SB calls $0.49

Flop: ($1.85) T:spade: Q:heart: 2:spade: (2 players)
SB checks, Hero bets $1, SB calls $1

Turn: ($3.85) T:club: (2 players)
SB checks, Hero checks

River: ($3.85) 4:spade: (2 players)
SB checks, Hero bets $4.13 all in, SB folds

Did hero play this hand correctly?

Why such a small 4bet? If he had 5bet, what would you have done? (not saying it was wrong, just want to know what you were trying to do)

Flop bet, fine. Turn.... hmmm, T dosent change anything, so if he calls OTF, I guess checking behind is ok here.

River, maybe small-ish, to look more bluffy and give an illusion of FE, get shoves from Tx-Qx hands?

I thought 2.2x was a pretty standard 4bet size? I need to make it look like I'm not pot-committed, so that the villain could think there's a possibility that I'm 4bet bluffing (which I do sometimes too). And if villain 5bet shoves then I'm snap-calling. I definitely don't expect his shoving range to be only KK+ in a blind vs button war.

I thought that shoving the river would look far more bluffy than betting small, hence why I shoved. Betting small looks like I'm seeking value.

Yeah, 2.5x is standard 4-bet size. Your bets are a little small. You'd like to size it so you have about a pot-sized bet left on the river, and your bet size came in a little large.

Hand is fine, just a minor sizing complaint.