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/tests/commands/random/int.rs

@@ -2,21 +2,21 @@ use nu_test_support::nu;
 
 #[test]
 fn generates_an_integer() {
-    let actual = nu!("random integer 42..43");
+    let actual = nu!("random int 42..43");
 
     assert!(actual.out.contains("42") || actual.out.contains("43"));
 }
 
 #[test]
 fn generates_55() {
-    let actual = nu!("random integer 55..55");
+    let actual = nu!("random int 55..55");
 
     assert!(actual.out.contains("55"));
 }
 
 #[test]
 fn generates_0() {
-    let actual = nu!("random integer ..<1");
+    let actual = nu!("random int ..<1");
 
     assert!(actual.out.contains('0'));
 }

crates/nu-command/tests/commands/random/mod.rs

@@ -2,6 +2,6 @@ mod bool;
 mod chars;
 mod dice;
 mod float;
-mod integer;
+mod int;
 #[cfg(feature = "uuid_crate")]
 mod uuid;

crates/nu-command/tests/commands/url/join.rs

@@ -245,7 +245,7 @@ fn url_join_with_invalid_port() {
 
     assert!(actual
         .err
-        .contains("Port parameter should represent an unsigned integer"));
+        .contains("Port parameter should represent an unsigned int"));
 
     let actual = nu!(pipeline(
         r#"
@@ -259,7 +259,7 @@ fn url_join_with_invalid_port() {
 
     assert!(actual
         .err
-        .contains("Port parameter should be an unsigned integer or a string representing it"));
+        .contains("Port parameter should be an unsigned int or a string representing it"));
 }
 
 #[test]