Thanks for taking a look, I appreciate the explanation!
I just want to clarify something, if you don't mind, because I'm not sure I'm understanding why the shoe_size wouldn't be captured by reference. It seems like an immutable reference would be the least amount of access needed so that would be what gets used, like how it's described in part of section 13.1: Capturing References or Moving Ownership. I decided to try out the following, which I think would work if shoe_size was copied instead of captured as a reference:

let mut shoe_size: u32 = 9;
let shoe = Shoe { size: 7, style: String::from("sandal") };

let f = |s: &Shoe| s.size == shoe_size;

let shoe_size_ref_mut = &mut shoe_size;
f(&shoe);

but I get the following error when I try to do so:

error[E0502]: cannot borrow `shoe_size` as mutable because it is also borrowed as immutable
  --> src/shoe.rs:13:29
   |
11 |     let f = |s: &Shoe| s.size == shoe_size;
   |             ----------           --------- first borrow occurs due to use of `shoe_size` in closure
   |             |
   |             immutable borrow occurs here
12 |
13 |     let shoe_size_ref_mut = &mut shoe_size;
   |                             ^^^^^^^^^^^^^^ mutable borrow occurs here
14 |     f(&shoe);
   |     - immutable borrow later used here

For more information about this error, try `rustc --explain E0502`.
error: could not compile `playground` (bin "playground") due to 1 previous error

I ended up taking a look at the reference, and this section gave me a bit more confidence in my understanding of it:
https://doc.rust-lang.org/reference/types/closure.html#capture-modes

The compiler prefers to capture a closed-over variable by immutable borrow, followed by unique immutable borrow (see below), by mutable borrow, and finally by move. It will pick the first choice of these that is compatible with how the captured variable is used inside the closure body. [...]
If the move keyword is used, then all captures are by move or, for Copy types, by copy, regardless of whether a borrow would work.

So I think that if move had been used then shoe_size would have been copied as you said. Or if all of the borrows weren't compatible with how it was used in the closure then it would also be moved.

It's also very possible I'm misunderstanding something about the borrow checker. If so then my apologies and please let me know if that's the case! 😅