Here is an example of a line that I have trouble with.

When my opponent made a pot-sized 3-bet I thought I had good enough pot odds to call but I decided to just ship it since I really don't like x/f-ing blank turns from an equity realization standpoint, especially at this stack depth.

Obviously in this hand I did manage to get there and make a flush but I'm not sure whether my all-in was a good decision. I'm only ever getting called by top pair and also some 2 pair and sets so it seems like I almost never have more than a 40% chance to win the hand. Also it seems to me given my (limited) experience the players in my pool aren't taking this line with bluffs and I'm really not likely to ever get folds with my 4-bet all in.

Could I have found a fold or a call? What are some heuristics I can use to help me make decisions in these spots? How does size of the effective stack change these decisions, if at all?

In limp pots, it's advantageous to get the initiative by betting on the flop yourself. You can do this with any pair or draw.
The exception is your opponent's extremely aggressive and very rarely folds postflop.

As played - Check/Call on the Flop.
Keep the pot small with your dominated flush draw, aiming to extract maximum value from your opponent if you hit your flush on a later street.

Thanks for the advice about betting flop in limped pots. I practically never bet flop from the BB in limped pots so this is definitely a leak. Can you elaborate on the theoretical basis for constructing my betting range in the way you suggest so that I can intuitively understand it better? I guess the justification would be that we protect all of our pairs and gain fold equity/bloat the pot with our draws?

I know that in SRPs BB vs IP solvers will play at least some x/r with almost all flush draws. Why do we prefer to play check/call for pot control in this spot as played?

In theory it’s fine to checkraise flush draws (and even to jam over a 3bet), but that’s because the solver assumes that you have some fold equity.

Take a look at what IP is supposed to be 3betting. There are lots of crappy hands like bottom pair that are 3bet/folding - something that might not be happening in practice. So in reality it’s probably closer between calling and folding (as opposed to calling/jamming).

Checkraising can be fine given the right type of opponent though (stabbing a lot and folding to raise). The key is that for these aggressive plays to work, you need fold equity.

^ thanks this makes a lot of sense. Definitely not seeing a lot of 3b/f in practice.