I think you just prefer to x/r on the flop than x/r on the turn because you will have more value hands if you x/r otf than x/r ott (not sure if this is really good to x/r J6s or T6s ott but x/r these kind of combos on the flop is totally ok). Considering this, you will have the possibility to x/r more on the flop.
This is also good to x/r turn, but I really prefer to make this on the flop. Also, you can play the hand as you played it, which is ok I guess.

This is kind of a cash game spot since you have very deep stacks.

In a BTN vs BB scenario with antes, you have pretty wide ranges. BTN probably has some range advantage and nut advantage here because he has all the sets and all the overpairs while you don't. The flop is multiway, so BTN should have a slightly stronger range to c-bet. So you should be check-raising with a polarized range (if you elect to check-raise). This hand is fine to do so, since you can barrel turn to put a lot of pressure on his weak range.

But check-calling is fine as well. With this hand, you can easily check-call down to the river, so you'll never get blown off your equity.

Another option is to check-raise flop and check turn. If opponent bets turn, you can check-raise again. Though double check-raise is fancy play, your hand has a lot of equity no matter what.

Usually, when two or three options are close like this, you want to take a mix of all.

I'd probably check raise flop, I'm fine with not having a raising range on this flop because we don't have any of the top 2 sets and not all of the 2 pairs (T6 and J6o I'm assuming were folded pre), having said that if you are going to raise your set and 2 pairs here you need some bluffs and this is pretty much the best one (I imagine KQs gets 3B pre). I prefer having a raising range at lower stacks due to station opponents that I want to stack off light and often with so yeah I'd raise this.

If we don't raise the flop I don't like the raise on the turn, this is because none of your flatting hands have now become premium hands that you want to raise, you're basically saying that you slow played the flop, which once again is fine if you never raise this flop but villain doesn't know that so they're left staring at your check raise and probably come to the right conclusion, you're on some kind of combo draw.

On the river I really don't hate leading this, you don't have AK but you do have K9, 98, QJ, QT, KQo so you have a lot of fairly nutted hands that want to lead and I don't mind adding in Q9/Q8 as well here. This is very villain dependent, if they're the kind of player that is likely to raise the river as a bluff this is probably suicide for your winrate and you should stick to leading with a very polarised range if at all here but as we are assumedly calling a reasonable sized bet I think we should look for thin value from a jack here. QJ is probably too tight for bet flop and bet turn with how tight multiway ranges should be so I don't think villain has improved here unless he has QQ which there is 1 combo of and if we can comfortably fold to a raise knowing villain isn't doing it without the nuts then we can skirt then line between blocker and value bet here with something like 1/3 pot. Just something I like to add into my game against opponents that lack creativity because those small river bets are actually really big (1/3 pot on the river is larger than the 60% pot bet on the turn) so you're gaining around 13BB when you're good and saving yourself 13BB when you face a 2/3 pot bet when you're not. If you were intending to fold Q9 to a triple barrel here then this isn't as relevant but I think it's probably one of your best bluff catchers, you block the straight and are probably at the top of your range if you like to lead this river when you improve to 2pair+. Don't do this kind of thing against people that you play with regularly though because it only takes one showdown for them to go home and work on their river bluff raising range in order to exploit you.