Normally I wouldn't even respond to such a poorly structured OP, but the "first reply" answer is some of the worst I have ever on this forum so felt I had to give a proper response.
The hand vs range match can be broken down into 3 quite distinct categories:
They have a tier1 hand (flush) and will be betting for you given that you repped the straight and the flush came in meaning that they will perceive themselves to have some FE, EV of betting <= EV of checking assuming it's not someone who will bet 1/6th pot with the 2NF and fold to a raise assuming you have to have it 100% of the time. You would have gotten more by betting a size > 1/6th pot and being called.
They have a tier2 hand which is the same broadway straight you had on the turn before you hit your redraw. They will either checkback hoping you dont have a flush (scared money) or bet trying to get you off the same nut straight that you repped on the turn. You lose when he checks back broadway and was planning on still calling a bet despite the flush coming in and you gain when they will bluff with the nut straight or worse here.
They have a tier3 hand so a set or worse and will bluff at it some % of the time, given that you made no mentions of the action on the flop, this seems super unlikely.
In nut straight vs nut straight scenarios in most player pools when you are OOP and the flush comes in you should generally be checking when you hit and betting/shoving when you don't, this is assuming your opponent is the type of player who will always shove nuts + redraw at low SPRs when you wouldn't be able to get away even if cards were face up and you could see that you are getting freerolled.
Poker Stars, $2.50/$5 No Limit Omaha Cash, 6 Players
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#37809178
BTN: $2,407.52 (481.5 bb)
Hero (SB): $676.66 (135.3 bb)
BB: $1,437.59 (287.5 bb)
UTG: $1,653.34 (330.7 bb)
MP: $1,351.75 (270.4 bb)
CO: $481.99 (96.4 bb)
Preflop: Hero is SB with Q
J
9
K
4 folds,
Hero raises to $15, BB calls $10
Flop: ($30) 7
A
8
(2 players)
Hero checks, BB checks
Turn: ($30) T
(2 players)
Hero bets $24.23,
BB raises to $81.18,
Hero raises to $272.04, BB calls $190.86
River: ($574.08) 2
(2 players)
Hero bets $389.62,
BB folds
Results: $574.08 pot ($3 rake)
Final Board: 7
A
8
T
2
Hero mucked Q
J
9
K
and won $571.08 ($284.04 net)
BB mucked and lost (-$287.04 net)
How not to allow yourself to get freerolled to a chop on texture changing rivers OOP.