I misread the stack-depth, and I think that it might be too loose, in which case I believe that with my hand in particular I should maybe cbet flop and turn. But I am trying to read the situation to see if it's a good check-shove spot.

Even though villain shows passive tendencies I think our hand is too good to give up on the flop, but I'm reluctant to bet the flop due to villain being able to float with a lot of strong broadway spades or clubs, in which case my hand is almost always bad on the turn and I don't really know what to do there. But I think I should call the cbet since villain can have a lot of missed overcards, and folding top pair here seems way too tight. Also, if villain is passive she might give up on turns like this one and I can realize my equity (somewhat contradicts the previous sentence but I not overly so).

But given a low turn bet, I don't think I can call with my hand since I can easily be outdrawn. Yet I think villain can still bet a lot of hands which I beat. So a turn shove should put every draw in a horrible spot, and potential folds from A9, TT. I need about 53% fold equity to make it outright profitable, which I'm not sure if I have.

The hands that beat us are 44-55, 88+, A9, 89. Villain may be capped due to not 4 betting preflop, making it fewer combos.

Do you think I'm overplaying my hand here? If I so, what other path could I have taken with the hand?