Integrates signup and signin with Zustand auth store

[mano-ranjan]

🚀 Summary

Integrates signin and signup to use zustand's auth store instead of doing it on UI level

🧩 Related Issues / Tasks

Closes #30

🛠️ Type of Change

• 🐞 Bug fix
• ✨ New feature
• 🧨 Breaking change
• 🔨 Enhancement/Refactor
• 📝 Documentation
• 📜 Other (please describe):

✅ Checklist

• The code is formatted with Prettier (npm run format or npx prettier --write .)
• PR references a linked Issue or Task number
• Tested on both iOS and Android devices/emulators
• No unnecessary logs or commented-out code
• UI changes, if any, have been reviewed visually
• All tests are passing (if applicable)
• Added or updated documentation where necessary

🧪 Test Plan

1. Signin if already having an account, it seamlessly routes the user to the welcome screen and then further to homescreen
2. Signup by entering valid info, it routes the user to welcome screen and then homescreen