His range hits the board pretty well, so does mine

His likely hits this better as we have more air hands compared to him. When the 3-bet cold caller continues on this board against a decent sized flop cbet you have to be careful.

Usually I'd go for a range bet, but decided to mix in a little larger 60% bet, I guess all options are fine here except check.

Multiway as well. We can bet smaller and get the same folds/calls. So the main reason to go bigger is for value. Which would target UTG more. Once UTG folds and SB calls, be careful.

My plan on a hand was to either check turn/call river or bet
turn/check river. I guess after my turn bet I am so what meant to call
any jams with my given hand, or not?

It's more likely that SB has a showdown heavy hand compared to a hand SB would want to turn into a bluff. So turn bet and evaluate river seems better. When he jams we should have to call a bunch in theory. But in practice it seems so unlikely that he is bluffing here. Our hand looks exactly what it is and still he raises. Fold this and call other hands. QQ blocks KQs for his bluffs as well.

How do you percieve these spots? What advice you'd give me on
constructing my range otf/ott, what size to use?

I would go smaller on flop despite not range betting. QQ does want to bet quite often.

Check flop. If you bet it has to be small 1/4 Pot.