I wonder if this would apply to squeeze spots as well?

100BB opens UTG, 200BB calls BTN and it's to you in the BB with 200BB

It's not a linear relationship.
Basically OOP you want to be able to set up an SPR in which you can end up all in on the turn so you can avoid Equity switches without making villains range too equity driven. EQ switches are very bad OOP because It turns our strong hands into bluff catchers which lose the pot every time they face a bet.
Usually you achieve this by 3betting bigger deeper, but at some stack depth the 3bet would be so huge that all of villains range that calls would have good equity/implied against our overpairs, therefor we start 3betting smaller to keep villains calling range weak and dominated so we can play postflop with less bluffcatchers in range

As a follow up, I'm kind of intrigued as to whether being deep (200bb+) changes 4bet and 5bet frequencies, as well as calling frequencies. At 200bb deep, you can 5bet jam, but you're not getting great odds, so I was thinking that 5betting might be to a non-allin size. Especially if 3betting to smaller sizes. Then, when even deeper (300bb+), is jamming pre still a thing, or do we just call 4 or 5bets with our whole continuing range?

In this case, you're much more likely to be called/raised by UTG so I would imagine this plays closer to 100bb effective.

The 4b/5b lines are extremely overpair heavy, so it makes sense that the strategy would largely revolve around that hand class. Though I'm not convinced it always comes down to tryna set up a turn shove.

How does one go about trying to study "equity switches"? More generally, how do we measure how "dynamic" a board is?

I think a lot of players simplify to pure flatting ranges at some point, but in equilibrium jamming ranges are still a thing 200-300bb deep. Non all-in 5b ranges are definitely a thing deeper stacked, though it sounds like a nightmare to play from a human perspective lol.

You can check out the 4b frequencies in the links above, though they aren't normalized.

I have equity switches more in class with ev switches. I your range is 43 ev vs 7 ev of caller, you want to maintain that edge. But, you need to study different flop textures to know when to push that edge, and how different flop textures change that ev.

Some flops are good for the caller, and they will check to you vs donking, you need to be careful with the cbet here. My opinion.

It's something that happens across the board on all kinds of OOP spots. Your first alternative to avoid tought spots is to size up to have the option to not play 3 streets, and when SPR doesn't allow it, you size back down to make those tough spots less tough against weaker ranges