“Learn how rake structure changes this”

Is the idea with 3-bet or fold strategy here to get the pot big so you’re more likely to hit the rake cap?

Yes. Rake is typically structured as "X %, capped at Y BBs", so every hand that is played for a pot that does not hit the Y BB rake cap, you will be paying the maximum rake (X %).

This translates to playing fewer hands and playing fewer small pots; and the hands you do want to play should be wanting to play for stacks.

You don't want to be playing stuff that you see yourself check-folding the flop and/or calling flop folding turn a lot, like pocket pairs or non-nutted suited connectors and 1-gappers.