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

@@ -0,0 +1,22 @@
+use nu_test_support::nu;
+
+#[test]
+fn generates_an_integer() {
+    let actual = nu!("random int 42..43");
+
+    assert!(actual.out.contains("42") || actual.out.contains("43"));
+}
+
+#[test]
+fn generates_55() {
+    let actual = nu!("random int 55..55");
+
+    assert!(actual.out.contains("55"));
+}
+
+#[test]
+fn generates_0() {
+    let actual = nu!("random int ..<1");
+
+    assert!(actual.out.contains('0'));
+}