[Phase 2] Enhance TeamChannelSelector with Complete Filtering and Search

[halsk]

Description

Enhance the TeamChannelSelector component with full filtering, search, and pagination capabilities.

Prerequisites

• [Phase 1] Create TeamChannelSelector Component ([Phase 1] Create TeamChannelSelector Component #172)

Tasks

• Implement search functionality for channel names
• Add loading states and error handling
• Delete channel settings icon
• Add filters for channel type (public, private, etc.)
• Show Member Count (Now member count is Unknown)
• Ommit archived channels from the list
• Implement client-side pagination
• Add sorting options
• Optimize for performance with large channel lists
• Move analysis and analysis history icon to the Selected Channels pane
• Hide analysis and analysis history icon if the channel doesn't have bot installed

References

• Based on strategy document in PR Add Channel Analysis UI Strategy Document #171
• Reference existing filtering in ChannelList.tsx

Acceptance Criteria

• Users can search for channels by name
• Filtering by channel type works correctly
• Pagination controls work for large channel lists
• UI is responsive and performance is acceptable
• Loading and error states are properly handled
• UI is consistent with existing components