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/formats/to/nuon.rs

@@ -97,7 +97,7 @@ impl Command for ToNuon {
                 result: Some(Value::test_string("[1, 2, 3]"))
             },
             Example {
-                description: "Outputs a NUON array of integers, with pretty indentation",
+                description: "Outputs a NUON array of ints, with pretty indentation",
                 example: "[1 2 3] | to nuon --indent 2",
                 result: Some(Value::test_string("[\n  1,\n  2,\n  3\n]")),
             },