Fixes#1364
<!-- CURSOR_SUMMARY -->
> [!NOTE]
> Refreshes the Supabase prompt’s login state example to use the latest
onAuthStateChange event handling and unsubscribe pattern.
>
> - **Prompts**:
> - **Supabase system prompt (`src/prompts/supabase_prompt.ts`)**:
> - Revise login state management example to use
`supabase.auth.onAuthStateChange` with explicit events:
`INITIAL_SESSION`, `SIGNED_IN`, `SIGNED_OUT`, `PASSWORD_RECOVERY`,
`TOKEN_REFRESHED`, `USER_UPDATED`.
> - Update unsubscribe usage to `data.subscription.unsubscribe()` and
remove outdated async/getSession snippet.
>
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<!-- /CURSOR_SUMMARY -->
fixes#1010
<!-- This is an auto-generated description by cubic. -->
---
## Summary by cubic
Disable automatic JWT verification for Supabase Edge Functions and
update prompts/templates to require and demonstrate manual auth
handling. Fixes#1010.
- **Bug Fixes**
- Set verify_jwt: false in function deployment.
- Updated Supabase prompt with an Authentication section and guidance to
manually verify tokens.
- Adjusted the hello function template to check the Authorization header
and return 401 when missing.
<!-- End of auto-generated description by cubic. -->
