Refactor parser methods to not return State as part of ParseError

As previously discovered with #4464, it's easy to accidentally mis-use the State value returned on the Err path.

There were mixed assumptions about what that State represents: (1) the State where the error occurred, or (2) the State at the beginning of the thing we were just parsing.

I fixed this up to always mean (2) - at which point we don't actually need to return the State at all - so it's impossible for further discrepency to creep in.

I also took the liberty to refactor a few more methods to be purely combinator-based, rather than calling `parse` directly.

crates/compiler/parse/tests/test_parse.rs

@@ -846,7 +846,7 @@ mod test_parse {
             Ok((_, _, _state)) => {
                 // dbg!(_state);
             }
-            Err((_, _fail, _state)) => {
+            Err((_, _fail)) => {
                 // dbg!(_fail, _state);
                 panic!("Failed to parse!");
             }