Would fold preflop. Issue is that KQ with bad support is very easily dominated by SB range which should be somewhat on tight side. We would prefer to have two more low card with good connectivity, e.g. 7643ss.. As ds combo I would still call.
Flop seems like mandatory check as we have absolutely no interaction with flop. Sure some bd equity but we have that almost always in this game. Maybe with two bdfd we could think of stabbing but not sure of that.
I would probably not have raising range on turn at all. What strong hands do we have after flop check? Some AT perhaps but even those are usually without support. Which does not make that strong of a hand for deep SPR spot. Well I suppose some slowplayed TTJ9 type is possible. Point is though that it's lot easier for SB to have strong stuff. He might have looked for flop x-r and he also has AA which we basically never have. Plus some AKQT type possible as well though I think these hands are cbet very often. But also other solid Axxx, e.g. AKJ9.
Anyway on turn I would definitely fold without K♣: which open some bluff possibilities for river. Even with that it's probably fold to this big sizing. So if we call 4.8bb with 6 nut outs we have 14% chance to hit that on river. So we need as implieds around 20bb from villain in river with pot being 16bb. So that is huge implied requirement. Now of course we have two flush completing cards to hit straight but we can't value bet on those. We might bluff catch or raise versus bet I suppose. Evaluating EV of having chance to bluff bet or raise on flushing card is tough but usually these are marginally plus EV only .
In river I would raise J9 for sure versus this sizing. This might be reasonable river bluff as we have Q and K. Not sure how nut fd blocker plays in this though. Usually we don't want to block that as it's part of villain bluff range that would auto fold.
But yeah I would personally fold both pre and turn.