I seem to be having the same or a similar problem.
I've noticed that the watch does vibrate but only very faintly in sort of coughs and splutters.
If watch is on silent mode this means the alarm often doesn't wake me as vibration is too faint and sound never goes off on the phone.
If watch isn't in silent mode i will usually only notice the sound from the phone and not the vibration.
It did all work when i first got the watch ( watch se), so maybe it has been caused by an os update.
Also tried factory reset of watch as adviced by tech support but this made no difference.
Setting a normal alarm from my watch instead of using the sleep funtion has been my work around, i.e. not using the sleep app.
This seems to vibrate on the watch properly (enough to wake me) without making a sound if the watch is on silent mode.
I've also had to set the time of this alarm using siri as the touch interace didn't work chosing the time of alarm on the watch directly.
So a few bugs seem to be affecting my setup anyway.
I'm hoping it get's fixed as i quite liked the effect of vibration turning into sounds if i didn't wake ( when it used to work.)