Hi
How notifications behave depends on the status of your devices and your settings. With Wrist Detection enabled, in order to bring notifications to your attention as soon as possible:
- If your iPhone is unlocked, then you will receive notification alerts on your iPhone instead of on your Apple Watch.
- If your iPhone is locked or asleep and your Apple Watch is unlocked (regardless of whether the watch display is asleep or awake) and on your wrist, you will receive notification alerts on your watch.
- If your Apple Watch is locked or has Do Not Disturb enabled, then notifications will go to your iPhone.
More information:
Notifications on your Apple Watch - Apple Support
It texts are not being received as you expect, then it may help to follow the instructions here, including under the heading "Get help if you can't send or receive messages" and including unpairing and re-pairing your Apple Watch if necessary:
Read and reply to messages with your Apple Watch - Apple Support
Keep in mind that the functions that are available on your Apple Watch when it is away from your iPhone depend on various factors including:
- Your Apple Watch model:
- The features of your carrier service plan:
- The type of connectivity that is available to your Apple Watch at the time:
About Bluetooth, Wi-Fi, and cellular on your Apple Watch - Apple Support
Features and requirements that apply under various circumstances are detailed here, including within footnote #1:
How to use your Apple Watch without your iPhone nearby - Apple Support