Use int type name consistently (#10579)

# Description
When referring to the type use `int` consistently. Only when referring
to the concept of integer numbers use `integer`.

- Fix `random integer` to `random int` tests
  - Forgot in #10520
- Use int instead of integer in error messages
- Use int type name in bits commands
- Fix messages in `for` examples
- Use int typename in `into` commands
- Use int typename in rest of commands
- Report errors in `nu-protocol` with int typename

Work for #10332 

# User-Facing Changes
User errorrs should now use `int` so you can easily find the necessary
commands or type annotations.

# Tests + Formatting
Only two tests found that needed updating

crates/nu-cli/src/commands/commandline.rs

@@ -91,7 +91,7 @@ impl Command for Commandline {
                             from_type: "string".to_string(),
                             span: cmd.span(),
                             help: Some(format!(
-                                r#"string "{cmd_str}" does not represent a valid integer"#
+                                r#"string "{cmd_str}" does not represent a valid int"#
                             )),
                         })
                     }