Instead of using an alarm, how about using a timer? iOS only allows a single timer, so you don’t end up with a string of timers in the same way as alarms. If using iOS timers, just ensure that the notification sound is not set to Stop Playing otherwise you won’t get any sounds (this can’t be set in the Shortcut) and is persistent when set.
You could instead use an app like Just Timers where you can create new timers that “self destruct” once you silence them or create a specific nap timer if it is always of the same duration. Just remember to add the app to your Focus Mode to allow notifications or use the Critical Alerts feature in the timer and your Focus Mode. Just Timers can also run a Shortcut once the timer is complete, so it could turn off the background noise you have running and set the Focus Mode back to a different “non-nap” mode.
Hope this helps.