Rollup merge of #118888 - compiler-errors:uplift-more-things, r=jackh726

Uplift `TypeAndMut` and `ClosureKind` to `rustc_type_ir`

Uplifts `TypeAndMut` and `ClosureKind`

I know I said I was just going to get rid of `TypeAndMut` (https://github.com/rust-lang/types-team/issues/124) but I think this is much simpler, lol

r? `@jackh726` or `@lcnr`

compiler/rustc_errors/src/diagnostic_impls.rs

@@ -378,3 +378,9 @@ pub struct IndicateAnonymousLifetime {
     pub count: usize,
     pub suggestion: String,
 }
+
+impl IntoDiagnosticArg for type_ir::ClosureKind {
+    fn into_diagnostic_arg(self) -> DiagnosticArgValue<'static> {
+        DiagnosticArgValue::Str(self.as_str().into())
+    }
+}