How to have sleep schedule Wake Up alarm play only on bedside Watch?

I want to clear my bedroom from distracting electronic devices. That’s why I bought an Apple Watch (Ultra 3) so I can leave it on my nightstand and still be able to receive (emergency) calls during the night. I am not wearing the watch during the night, since I am not interested in sleep tracking (and the bulky watch will get in the way when cuddling with partner).

How can I use the Watch as an alarm without wearing it?

Summary: Watch on nightstand in bedside mode, iPhone in other room, want to be waken up from alarm on Watch

Things I have tried:

1. Set up alarm using the sleep schedule in Sleep Watch app.

This results in an alarm sound only being played on the iPhone. Just read in other discussions that this is expected behaviour. Some people want to use their iPhone for alarm while wearing the Watch. The Wake Up won’t happen from the Watch since it is locked, but play on the iPhone.

2. Set up alarm using the alarm Watch app while the Watch is charged.

Alarm goes off (volume is okay ish) and no haptics are used. Alarm sound cannot be changed, standard bell ringing.

3. Set up alarm using the alarm Watch app while disconnected from charger.

Very dim ringing bell. Volume does not seem to be configurable. Haptics work, resonates nicely through my nightstand.

Both 1 and 2 are not waking me up. The third wakes me because my nightstand resonated from the haptics, but I would rather have an (configurable) audio alarm. The speaker of the Watch is perfectly able to produce a sound level that would wake me.

How to have the sleep schedule alarm play only through my locked bedside watch?

Do I want something that is not possible?