fix: Resolve UI inconsistencies and formatting bugs

[kmanish527]

🚀 Pull Request Checklist

• ✅ My issue is assigned to me, and I have not taken up another task simultaneously.
• 🔁 I have pulled the latest changes from the main branch.
• 🧪 My code is tested and does not break existing functionality.
• 📚 I have added/updated documentation wherever necessary.
• 🧹 My code follows the project’s coding standards.
• ✍️ My commits are clear and meaningful.
• 🧾 I have linked the issue this PR addresses with Closes #202 .

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📌 Related Issue

Closes #202

🧠 Description

• Unifies the navigation bar across the Dashboard and Pomodoro pages to ensure a consistent look and feel.
• Corrects the authentication state for the homepage's floating navbar, allowing it to display the "Logout" button for logged-in users.
• Fixes a text-rendering bug in the profile update notification where Markdown was being incorrectly interpreted by JSX.

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✅ Type of Change

• 🐞 Bug fix
• 💡 Feature
• 🧹 Code cleanup/refactor
• 🧪 Test cases
• 📚 Docs update

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[github-actions]

🙌 Thanks @kmanish527 for raising this PR!
Our team will review it soon ⏳ — meanwhile, please make sure your PR follows our contributing guidelines 👉 Contributing Guidelines 🎉

[github-actions]

🎉🎉 Thank you for your contribution! Your PR #203 has been merged! 🎉🎉