Wear OS can place apps into the list of "Sleeping Apps". When that happens to Wake Up Well, it will not work correctly any more.
You can see the apps that were placed into the list of "Sleeping Apps" here:
Settings -> Battery and device care -> Battery -> Sleeping apps
If you see Wake Up Well in there, please remove it. Then it will be allowed to run in the background again.
The sensors of individual watches behave differently as far as sensitivity is concerned.
You can adjust the sensitivity of the sensors with the sensitivity setting in Wake Up Well.
To access it, open Wake Up Well on the watch, scroll all the way up until you see a small arrow at the top. Click on the arrow and select the gear icon. Search for Sensitivity in the list.
The values range is from -4 to 4. The value -4 causes it be be very insensitive, so you'll likely wake up in the end of the wake up window. As oposite, the value 4 is most sensitive so that you may wake up too early.
Likely you have a Samsung watch if the permission isn't there.
I contacted Samsung and they told me, that their watches don't support the permission "Display over other apps". Older Samsung software-versions are working, because in these versions there is no such permission yet. Samsung said, that it might be considered in the future. Please contact Samsung Chat support to also request it.
When the permission "Display over other apps" is not granted, Wake Up Well is unable to show the alarm screen spontanously.
As a workaround best use a watch face with so called Complications and place the Complication of Wake Up Well on the watch face. Then it's as easy as click there to open the alarm screen.
An other option is to slide up the screen when the alarm goes off and click on the notification of Wake Up Well.
The permission can be granted manually with adb. To set up adb, you can follow the Enable ADB Debugging steps. The permission is granted with the following command:
adb shell pm grant ch.pete.wakeupwell android.permission.SYSTEM_ALERT_WINDOW