feat: add search/filter to Projects tab in TUI

[ourines]

Summary

• Adds / key to enter search mode in the Projects tab
• Filters project list by name in real-time (case-insensitive substring match)
• Shows a live search input in the status bar with cursor indicator
• Disables the list's built-in filter and replaces it with a custom implementation

Key Bindings

Key	Action
/	Enter search mode
type	Append to query, filter list live
Backspace	Delete last character
Ctrl+U	Clear entire query
Enter	Confirm filter, exit search mode
Esc	Clear filter, restore full list
Tab	Clear filter, switch to next tab

Test plan

• Open TUI (codes), navigate to Projects tab
• Press / — status bar shows / █ cursor
• Type a partial project name — list filters in real time
• Press Backspace — last character removed, list updates
• Press Esc — full list restored, search bar disappears
• Press /, type query, press Enter — exits search mode, filter remains
• Press / while right panel is focused — should not activate search
• Press Tab during search — clears search and switches tab

Closes #35

Summary by CodeRabbit

• New Features
  • Added search functionality to the Projects tab—press "/" to activate search
  • Live filtering of projects as you type your search query
  • Search can be dismissed by pressing Enter or Escape

[coderabbitai]

Caution

Review failed

The pull request is closed.

📝 Walkthrough

Walkthrough

The PR introduces a search feature for the Projects tab in the TUI, allowing users to press "/" to activate search mode and filter projects by name in real-time. New state flags manage the search lifecycle, and helper methods handle incremental filtering and input processing.

Changes

Cohort / File(s)	Summary
Projects Tab Search Feature internal/tui/model.go	Adds searchActive and searchQuery state flags, wires "/" key to activate/deactivate search mode on Projects/Left focus, implements updateProjectSearch and applyProjectSearch helper methods for live filtering, integrates search rendering and lifecycle into Update and View methods, and handles backspace, clear, and quit actions during search.

Estimated code review effort

🎯 3 (Moderate) | ⏱️ ~20 minutes

Poem

🐰 With "/" we search through the project warren deep,
Filtering fast as the letters we keep,
No hopping around for the names that we seek,
Live search brings clarity, efficient and sleek!

✨ Finishing Touches

• 📝 Generate docstrings

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Post copyable unit tests in a comment
• Commit unit tests in branch feat/issue-35-tui-search

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