It is commonly known, that newer Huawei devices got issues with Connect Mobile.
The battery saving tools are killing the background process and Notifications are not being pushed to the watch anymore.
There is an option to exclude the Android battery saving mode:
Settings -> Apps & Notifications -> Apps -> Settings (Icon below) -> Special access -> Ignore Battery optimization -> Change "Allowed" to "All" to see Connect Mobile -> Tap & change
which not entirely work for Huawai devices.
But there is another thing, you can do! You can "Lock" the app from being killed in the Task-view:
This helped me and the Notifications are being pushed since a whole day without opening Connect Mobile manually.