Are you under 13? if yes, see:
About Sign in with Apple - Apple Support
"Sign in with Apple is not available for children under 13 years old. This age may vary by country or region. This age restriction doesn't apply to Managed Apple IDs."
If an app or feature on your device is not working, not appearing, or is restricted (grayed out), it may have been disabled using Screen Time, or by an IT administrator if you are using a device owned by an employer or educational institution.
- Read this support article If your Apple ID or other options are greyed out in Settings —> If your Apple ID is greyed out in Settings - Apple Support
Tap Settings > Screen Time > Content & Privacy > scroll to Allow Changes and turn on.
- If the device is managed (Settings > General > VPN & Device Management), contact the IT department that is doing the managing.