[Bug][Auth] Continue with email button is not responsive on sign-in screen

[Al629176]

Summary

On the sign-in screen, clicking 'Continue with email' does not trigger any action.

Steps to reproduce

1. Open the sign-in screen.
2. Enter a valid email address.
3. Click 'Continue with email'.

Expected

The email auth flow should start (OTP/magic link/next step UI).

Actual

Button appears clickable but no response is triggered.

Impact

• Blocks email-based authentication.
• New users cannot proceed through onboarding using email login.

Tasks

• Reproduce and capture frontend logs/network requests on button click.
• Verify button onClick handler is correctly wired.
• Validate form state/validation does not silently block submission.
• Check API request trigger path and error handling.
• Ensure disabled/loading states are visually correct.
• Add user-facing error if request fails.
• Add regression test for email sign-in CTA flow.

Acceptance criteria

• Clicking 'Continue with email' consistently starts auth flow.
• User sees clear loading/error/success states.
• Regression test covers this path.