fix(auth): add forgot password page

[Divv1524]

Issue Link

Closes #82

Changes Made

• Added a functional /forgot-password page matching the existing auth UI.
• Integrated forgot password API call with /public/api/v1/auth/forgot-password.
• Added validation, loading, success, retry, and API error states.
• Wrapped the actual frontend entry point with GoogleOAuthProvider so the login page renders correctly and the forgot password link can be used.

Type of Change

• Bug fix
• New feature
• Documentation update
• Code refactor

Testing Performed

Frontend Testing

• Component renders correctly
• Responsive layout checked through browser route testing
• No new console errors on forgot-password flow
• Production build passed

Test Cases:

• Direct /forgot-password route renders reset form.
• Empty email shows required validation and does not call API.
• Invalid email shows format validation and does not call API.
• Whitespace-only email is treated as empty.
• Valid email is trimmed before API submission.
• API success: false response shows inline error.
• HTTP error response shows backend error message.
• Successful API response shows confirmation message.
• “Try another email” returns to the form.
• Login page “Forgot Password?” link navigates to /forgot-password.

UI/UX Changes

• Added forgot password screen consistent with login/register design.
• Added inline success and error states.

Additional Notes

• npm.cmd run build passes.
• npm.cmd run lint could not run because the repo does not currently include an ESLint 9 eslint.config.js file.