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-cmd-lang/src/core_commands/for_.rs

@@ -199,7 +199,7 @@ impl Command for For {
     fn examples(&self) -> Vec<Example> {
         vec![
             Example {
-                description: "Echo the square of each integer",
+                description: "Print the square of each integer",
                 example: "for x in [1 2 3] { print ($x * $x) }",
                 result: None,
             },
@@ -209,7 +209,7 @@ impl Command for For {
                 result: None,
             },
             Example {
-                description: "Number each item and echo a message",
+                description: "Number each item and print a message",
                 example:
                     "for $it in ['bob' 'fred'] --numbered { print $\"($it.index) is ($it.item)\" }",
                 result: None,