Your exact problem is not clear to me. However, if the "Device Notification" command works when you run it manually on the device page but the same device does not do what you expect when used as the notification device somewhere in an app, then it likely suggests some problem with that app--or perhaps an issue with the device that is supposed to "wake up" or "trigger" that app.
So, some ideas:
verify that your water sensor does, in fact, show "water: wet" and "water: dry" when expected under "Current States" on the device page (in real time) or under "Events" on the device page (for a historical view)
verify the configuration of the app that is supposed to be sending the notification (did you choose the correct sensor, the correct notification device, etc.)--and especially if you set up something complicated like a Rule Machine rule, consider sharing it with the community to see if they can spot any problems
if the app you're using to do this has logs, consider turning them on for more information
To add / expand on @bertabcd1234 's suggestions, check the "is used by" section at the bottom of the device pages for the devices you expect to be involved, making sure the are the ones being used by the rule.
And here is the device going to wet, and then going to dry later. When the water is sensed by the device it gets activated and beeps. When I dry it out, it goes back to dry mode.
Do you have more than one hub? If you are not logged into the hub that initiates the notification I don't believe you will receive it... Doesn't explain some of your earlier experiences...
Actually, without any HSM experience.... does it not only notify you when there is a problem? So only when the water sensor becomes wet? Perhaps one for others to comment on...
Upgraded from 2.2.8 to 2.3 yesterday and this is working for me now. Not sure if it's due to a non advertised fix or the upgrade process, but if you are on older firmware try updating.