Switch all public types to non_exhaustive

This switches all public types to use non_exhaustive to make it easier
to make additions without a semver-breaking change.

Some of the ergonomics are hampered due to the lack of exhaustiveness
checking. Hopefully some day in the future,
non_exhaustive_omitted_patterns_lint or something like it will get
stabilized.

Closes https://github.com/rust-lang/mdBook/issues/1835

Cargo.toml

@@ -9,6 +9,9 @@ members = [
 all = { level = "allow", priority = -2 }
 correctness = { level = "warn", priority = -1 }
 complexity = { level = "warn", priority = -1 }
+exhaustive_enums = "warn"
+exhaustive_structs = "warn"
+manual_non_exhaustive = "warn"
 
 [workspace.lints.rust]
 missing_docs = "warn"