Add real-time processing status display to the browser UI at /user/page
showing indexed document count, pending queue size, and sync status.
Implements the status display described in ADR-007 lines 280-298.
Changes:
- Store document_queue and related state in app.state for route access
- Add _get_processing_status() helper to query Qdrant and check queue
- Display status section in user_info_html() with indexed/pending counts
- Show color-coded status badge (green "Idle" or orange "Syncing")
- Only displays when VECTOR_SYNC_ENABLED=true
Status appears in both BasicAuth and OAuth modes, positioned after
session info but before logout buttons. Numbers are formatted with
commas for readability.
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Co-Authored-By: Claude <noreply@anthropic.com>
