feat: Move background task indicators to status bar

[edenreich]

Moves background task indicators from the header and queue box to the status bar. Adds A2A task indicator to status bar configuration and removes separate background task display sections for cleaner UI.

Changes:

• Added a2a_tasks indicator to status bar configuration
• Added cost and git_branch indicators to status bar configuration defaults
• Removed background task display from header and queue box
• Added background task service to input status bar to show task count in status indicators
• Background tasks now appear in status bar instead of separate sections

Benefits:

• Cleaner UI with consistent status indicator placement
• Reduced visual clutter in header and queue box
• Better integration with existing status bar system
• More intuitive location for task status monitoring

[ig-semantic-release-bot]

🎉 This PR is included in version 0.90.0 🎉

The release is available on GitHub release

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