Hi there Jithuz,
It's expected not to receive notifications on both devices.
Notifications appear on your Apple Watch or iPhone, but not both.
If your iPhone is unlocked, you get notifications on your iPhone instead of your Apple Watch.
If your iPhone is locked or asleep, you get notifications on your Apple Watch, unless your Apple Watch is locked.
Learn more here: Notifications on your Apple Watch - Apple Support
If you're not receiving notifications on wither device, check the notification settings on your iPhone with the guidance here: Use notifications on your iPhone or iPad - Apple Support
Also, you'll want to be sure both your iPhone and Apple Watch are updated to the latest software versions, which are iOS 17.0.3 and watchOS 10.0.2. If needed, learn how to update both devices from the links below:
Update your iPhone or iPad - Apple Support
Update your Apple Watch - Apple Support
If this behavior persists, you'll want to reach out to Apple Support directly for further assistance. They're best-equipped to take a closer look at the issue and provide some additional guidance. This link will help you get started: Apple Support
Take care.