fix input signature of let/mut (#9695)

# Description

This updates `let` and `mut` to allow for any input. This lets them
typecheck any collection they do.

For example, this now compiles:

```
def foo []: [int -> int, string -> int] {
  let x = $in
  if ($x | describe) == "int" { 3 } else { 4 }
}

100 | foo
```

# User-Facing Changes
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# Tests + Formatting
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Make sure you've run and fixed any issues with these commands:

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crates/nu-cmd-lang/src/core_commands/let_.rs

@@ -17,7 +17,7 @@ impl Command for Let {
 
     fn signature(&self) -> nu_protocol::Signature {
         Signature::build("let")
-            .input_output_types(vec![(Type::Nothing, Type::Nothing)])
+            .input_output_types(vec![(Type::Any, Type::Nothing)])
             .allow_variants_without_examples(true)
             .required("var_name", SyntaxShape::VarWithOptType, "variable name")
             .required(

crates/nu-cmd-lang/src/core_commands/mut_.rs

@@ -17,7 +17,7 @@ impl Command for Mut {
 
     fn signature(&self) -> nu_protocol::Signature {
         Signature::build("mut")
-            .input_output_types(vec![(Type::Nothing, Type::Nothing)])
+            .input_output_types(vec![(Type::Any, Type::Nothing)])
             .allow_variants_without_examples(true)
             .required("var_name", SyntaxShape::VarWithOptType, "variable name")
             .required(

src/tests/test_parser.rs

@@ -623,3 +623,35 @@ fn def_with_input_output_broken_1() -> TestResult {
 fn def_with_input_output_broken_2() -> TestResult {
     fail_test(r#"def foo []: int -> { 3 }"#, "expected type")
 }
+
+#[test]
+fn def_with_in_var_let_1() -> TestResult {
+    run_test(
+        r#"def foo []: [int -> int, string -> int] { let x = $in; if ($x | describe) == "int" { 3 } else { 4 } }; "100" | foo"#,
+        "4",
+    )
+}
+
+#[test]
+fn def_with_in_var_let_2() -> TestResult {
+    run_test(
+        r#"def foo []: [int -> int, string -> int] { let x = $in; if ($x | describe) == "int" { 3 } else { 4 } }; 100 | foo"#,
+        "3",
+    )
+}
+
+#[test]
+fn def_with_in_var_mut_1() -> TestResult {
+    run_test(
+        r#"def foo []: [int -> int, string -> int] { mut x = $in; if ($x | describe) == "int" { 3 } else { 4 } }; "100" | foo"#,
+        "4",
+    )
+}
+
+#[test]
+fn def_with_in_var_mut_2() -> TestResult {
+    run_test(
+        r#"def foo []: [int -> int, string -> int] { mut x = $in; if ($x | describe) == "int" { 3 } else { 4 } }; 100 | foo"#,
+        "3",
+    )
+}