I would usually pick a size that a "T" would call, generally when they have the 8, they'll raise your bet anyway.
With this method, you 95% of the time still get max value when they have the bad straight(and they raise your river bet), and you still get called off by a "T" that may fold if you had bet big.
Most of the time you get best of both worlds with this line.
Yes if villain is actually passive that warrants a flop lead (in theory almost never as villain has all 2ps all sets, overpairs A9 advantage on this flop), you should bet river.
If villain isn't raising turns enough (JT, T8, T9, sets should be raising a lot), then this hand can/should overbet turn. I would either do that or x/r turn.
GTO/nodelocked optimal strat will maximize value with the nuts on such a dynamic board. If villain isn't putting in enough money then you should do it yourself.
GTO/nodelocked optimal strat will maximize value with the nuts on such a dynamic board. If villain isn't putting in enough money then you should do it yourself.