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-command/src/generators/seq_date.rs

@@ -283,8 +283,8 @@ pub fn run_seq_dates(
             Some(date) => date,
             None => {
                 return Err(ShellError::GenericError(
-                    "integer value too large".to_string(),
-                    "integer value too large".to_string(),
+                    "int value too large".to_string(),
+                    "int value too large".to_string(),
                     Some(call_span),
                     None,
                     Vec::new(),