I want to setup a new apple watch for my mother. as a family member. But most of the health apps such as ECG, Blood Oxygen etc.

Thanks for asking about the ECG feature.

Check here for availability in your region: ECG

ECG requires the current non-beta version of iOS and watchOS. For additional help with the ECG feature on your Apple Watch, take a look at these articles.

Heart rate notifications on your Apple Watch - Apple Support

Taking an ECG with the ECG app on Apple Watch Series 4 or later - Apple Support

If you have any other questions, please reach out to our team here: https://apple.co/HeartFeatures. If you believe that you are experiencing a medical emergency, please dial your local emergency services.

Take care.

Can't say why, but according to: Set up an Apple Watch for a family member - Apple Support

"The following features and apps are not available: irregular heart rhythm notifications, ECG, Cycle Tracking, Sleep, Blood Oxygen, Podcasts, Remote, News, Home, and Shortcuts."

Because for these features the watch requires it's own phone.