turned OESD standard spot 3b pot IP | do we develop a shoving range?

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turned OESD standard spot 3b pot IP | do we develop a shoving range?

Blinds: $1.00/$2.00 (6 Players) BN: $386.95 (Hero)
SB: $256.13
BB: $223.98
UTG: $110.23
MP: $221.90
CO: $342.53
Preflop ($3.00) Hero is BN with T Q
3 folds, Hero raises to $4.50, SB folds, BB raises to $22.50, Hero calls $18.00
Flop ($46.00) J 5 7
BB bets $13.98, Hero calls $13.98
Turn ($73.96) J 5 7 K
BB bets $49.85, Hero raises to $350.47 and is all in, BB folds
meh

Villain is a ((very))good regular and 3bets ME(!) 13% from BB vs BU

Preflop is close I guess and more often a fold IMO...

I call flop w backdoorpotential

OTT I am kinda "whatever"...
flushdraw and "scarecard" comes in - 2nd barrel freq goes up, my semibluffrange widens...

I am very undecided between calling (entire range) and shoving (a portion of our range)..

I think (dependent on villains tendencies) there are strong arguments to be made for both overall strategies..

Does anyone know how GTO approaches these spots?

Thank you for any thoughts!!

Kind regards

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