[Phase 2] Implement Authentication Context

[coderabbitai]

📋 Task Description

Authentication Context.

🎯 Objectives

• AuthContext + useAuth
• loggedInUser persistence + Remember Me
• Header integrates auth state

✅ Acceptance Criteria

• Login/Logout/Signup flows change state
• Backward-compatible with existing data

[github-actions]

👋 Thanks for opening this issue! We'll look into it as soon as possible, estimated time for response is 18–24 hrs.
If your issue goes stale beyond this timeframe, kindly contact mentors or PAs via our Discord server.

⏱️ Issue response & contact

• In the meantime, provide screenshots, videos, or other context to speed review and assignment.
• If relevant, please mention whether this issue is raised under GGSoC or OSCI when you create the issue.
• If you have questions, comment below or ping any mentor on discord.

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📝 Guidelines for Raising Issues

To ensure quality moving forward:
For UI/UX contributions

• You must include a design (Figma link, image, or wireframe) when raising an issue (if applicable).
• Issues without visual references will not be accepted.
• If the change is a modification, share screenshots of the area you want to change.
  For Backend contributions
• You must share a brief execution plan what you intend to build, how it works, and why it's needed.
• Vague issues will be closed without review.

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📝 Guidelines for Opening Pull Requests

• Your PRs should target the master branch.
• No one is allowed to push directly to main.
• All PRs which do not mention an issue will be closed without review.
• Do NOT raise a PR unless the issue is assigned to you.

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✅ Quick checklist (please attach before requesting assignment)

• Design link or screenshot (for UI/UX)
• Execution plan (for backend)
• Mention if this is under GGSoC / OSCI
• Any related issue/PR numbers referenced

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Happy contributing 🚀

[coderabbitai]

Blocked by: #1051 #1054

[coderabbitai]

Blocks: #1056 #1059