Make auto-cd check for permissions (#12342)

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# Description
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I was playing around with auto-cd and realised it didn't check for
permissions before cd'ing. This PR fixes that.

```
~/CodingProjects/nushell> /root                                                                           
Error: nu:🐚:io_error

  × I/O error
  help: Cannot change directory to /root: You are neither the owner, in the group, nor the super user and do not have permission
```

This PR also refactors some of the filesystem utilities to nu-utils,
specifically the permissions checking and users.

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crates/nu-cli/src/repl.rs

@@ -23,7 +23,10 @@ use nu_protocol::{
     report_error_new, HistoryConfig, HistoryFileFormat, PipelineData, ShellError, Span, Spanned,
     Value, NU_VARIABLE_ID,
 };
-use nu_utils::utils::perf;
+use nu_utils::{
+    filesystem::{have_permission, PermissionResult},
+    utils::perf,
+};
 use reedline::{
     CursorConfig, CwdAwareHinter, DefaultCompleter, EditCommand, Emacs, FileBackedHistory,
     HistorySessionId, Reedline, SqliteBackedHistory, Vi,
@@ -761,6 +764,16 @@ fn do_auto_cd(
         path.to_string_lossy().to_string()
     };
 
+    if let PermissionResult::PermissionDenied(reason) = have_permission(path.clone()) {
+        report_error_new(
+            engine_state,
+            &ShellError::IOError {
+                msg: format!("Cannot change directory to {path}: {reason}"),
+            },
+        );
+        return;
+    }
+
     stack.add_env_var("OLDPWD".into(), Value::string(cwd.clone(), Span::unknown()));
 
     //FIXME: this only changes the current scope, but instead this environment variable