I clicked Send code but nothing on screen changed — did a code actually get sent?

It usually did. After you click Send code the button locks for a few seconds (so a stray double-click can't accidentally invalidate the code already on its way), and the app watches for Supernote's confirmation — a green "A code has been sent to your email — enter it below" message above the code box. If no confirmation shows up within a few seconds, you'll see a neutral "Check your email — use Resend if nothing arrives" note instead, so you're never left guessing. Check your inbox (and spam), then type the code into the box below the email field. The button flips to "Resend code" with a countdown before you can request another.