Apple Support app not working with strong Wi-Fi connection

Restart your equipment and/or sign in out and back in again, and try again.

If you can't connect, Apple has a list of things you can try in the document If you can't connect or sign in to iCloud - Apple Support

Is the server working? --> https://www.apple.com/support/systemstatus

If you are using a VPN try removing it completely (don't just turn it off) and see if you can then use the service. E.g., AppStore - Apple Community

If you still have problems try official Apple Support. Click here --> https://support.apple.com/choose-country-region Select your country, then a product. If you don't see one that handles your issue then keep experimenting with selections until you reach one that gets you a chat session or a telephone call and get the representative to redirect you.

or:

Contact Apple for support and service --> "See a list of Apple phone numbers around the world."

Click here --> https://support.apple.com/HT201232

Do you have a VPN installed on your iPhone? If yes, get rid of it.

If the server is not working then you will have to wait until it is.