Use fn ptr signature instead of {closure@..} in infer error

When suggesting a type on inference error, do not use `{closure@..}`.
Instead, replace with an appropriate `fn` ptr.

On the error message, use `short_ty_string` and write long types to
disk.

```
error[E0284]: type annotations needed for `Select<{closure@lib.rs:2782:13}, _, Expression<'_>, _>`
  --> crates/lang/src/parser.rs:41:13
   |
41 |         let lit = select! {
   |             ^^^
42 |             Token::Int(i) = e => Expression::new(Expr::Lit(ast::Lit::Int(i.parse().unwrap())), e.span()),
   |                                                                                                  ---- type must be known at this point
   |
   = note: the full type name has been written to '/home/gh-estebank/iowo/target/debug/deps/lang-e2d6e25819442273.long-type-4587393693885174369.txt'
   = note: cannot satisfy `<_ as chumsky::input::Input<'_>>::Span == SimpleSpan`
help: consider giving `lit` an explicit type, where the type for type parameter `I` is specified
   |
41 |         let lit: Select<for<'a, 'b> fn(tokens::Token<'_>, &'a mut MapExtra<'_, 'b, _, _>) -> Option<Expression<'_>>, _, Expression<'_>, _> = select! {
   |                +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
```

instead of

```
error[E0284]: type annotations needed for `Select<{closure@/home/gh-estebank/.cargo/registry/src/index.crates.io-6f17d22bba15001f/chumsky-1.0.0-alpha.6/src/lib.rs:2782:13: 2782:28}, _, Expression<'_>, _>`
  --> crates/lang/src/parser.rs:41:13
   |
41 |         let lit = select! {
   |             ^^^
42 |             Token::Int(i) = e => Expression::new(Expr::Lit(ast::Lit::Int(i.parse().unwrap())), e.span()),
   |                                                                                                  ---- type must be known at this point
   |
   = note: cannot satisfy `<_ as chumsky::input::Input<'_>>::Span == SimpleSpan`
help: consider giving `lit` an explicit type, where the type for type parameter `I` is specified
   |
41 |         let lit: Select<{closure@/home/gh-estebank/.cargo/registry/src/index.crates.io-6f17d22bba15001f/chumsky-1.0.0-alpha.6/src/lib.rs:2782:13: 2782:28}, _, Expression<'_>, _> = select! {
   |                ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
```

Fix #123630.

compiler/rustc_infer/src/errors/mod.rs

@@ -18,6 +18,8 @@ use crate::infer::error_reporting::{
     ObligationCauseAsDiagArg,
 };
 
+use std::path::PathBuf;
+
 pub mod note_and_explain;
 
 #[derive(Diagnostic)]
@@ -47,6 +49,9 @@ pub struct AnnotationRequired<'a> {
     pub infer_subdiags: Vec<SourceKindSubdiag<'a>>,
     #[subdiagnostic]
     pub multi_suggestions: Vec<SourceKindMultiSuggestion<'a>>,
+    #[note(infer_full_type_written)]
+    pub was_written: Option<()>,
+    pub path: PathBuf,
 }
 
 // Copy of `AnnotationRequired` for E0283
@@ -65,6 +70,9 @@ pub struct AmbiguousImpl<'a> {
     pub infer_subdiags: Vec<SourceKindSubdiag<'a>>,
     #[subdiagnostic]
     pub multi_suggestions: Vec<SourceKindMultiSuggestion<'a>>,
+    #[note(infer_full_type_written)]
+    pub was_written: Option<()>,
+    pub path: PathBuf,
 }
 
 // Copy of `AnnotationRequired` for E0284
@@ -83,6 +91,9 @@ pub struct AmbiguousReturn<'a> {
     pub infer_subdiags: Vec<SourceKindSubdiag<'a>>,
     #[subdiagnostic]
     pub multi_suggestions: Vec<SourceKindMultiSuggestion<'a>>,
+    #[note(infer_full_type_written)]
+    pub was_written: Option<()>,
+    pub path: PathBuf,
 }
 
 // Used when a better one isn't available