[FEATURE]: Improve error handling and UX for GitHub organization search

### Feature and its Use Cases

Problem Statement

Currently, when users search for an invalid or non-existing GitHub organization, the application feedback can be improved for a better user experience. Some error states may appear unclear or not provide enough guidance to users.

Features / Suggested Improvements

Add clear and user-friendly error messages
Improve loading and error UI states
Handle invalid or empty organization names gracefully
Provide retry guidance or suggestions to users
Improve consistency of error handling across the application

Use Cases

User enters a non-existing GitHub organization name
User submits an empty search request
GitHub API request fails due to network/API issues
User mistypes organization name and needs clearer feedback
Improve overall usability and accessibility of search functionality

Benefits

Better user experience
More informative feedback handling
Improved usability and accessibility
Cleaner and more consistent UI behavior

### Additional Context

_No response_

### Code of Conduct

- [x] I have joined the [Discord server](https://discord.gg/hjUhu33uAn) and will post updates there
- [x] I have searched existing issues to avoid duplicates