How do I send Sound Recognition notifications from my ipad, to my iPhone?

Sound recognition is an Accessibility feature that works only upon the device upon which it is configured. These locally generated alerts cannot, to my knowledge, be natively forwarded to other devices.

Recognize sounds using iPad - Apple Support

You can create a new Automation from Shortcuts, setting the Sound recognition as a trigger, then send you a message that will appear on all your devices (you need to create a separate shortcut for this, in advance).

Unfortunately this doesn't work with custom sounds.