feat: Real-time Git Status Integration (#8)

* feat: implement real-time git status integration

- Add workspace tracker to monitor git changes every 2 seconds
- Implement WebSocket streaming for git status updates
- Add database persistence for git status in agent session metadata
- Compute diffs backend-side with additions/deletions per file
- Integrate git status into frontend UI (top bar, files panel, changes panel)
- Display real-time ahead/behind commits and line changes
- Show file diffs with syntax highlighting in task view
- Add retry logic for WebSocket connections during reconciliation
- Fix context lifecycle issue in workspace tracker

* refactor: remove debug and unnecessary logging

- Remove debug logs from workspace tracker
- Remove info logs from WebSocket handlers
- Remove verbose git status update logs
- Keep only essential error logs

* fix: compare git diff against remote branch instead of HEAD

- Changed git diff comparison from HEAD to remote tracking branch
- Now shows all changes including committed files that haven't been pushed
- Files committed locally but not pushed will appear in the diff
- Falls back to HEAD if no remote branch is configured

* fix: prevent stale git status when switching tasks

- Clear git status when switching to a new task
- Only accept git.status WebSocket updates for the current task
- Prevents showing git data from previous task when switching

* refactor: remove unused diff stream client code

- Remove diffConn field from agentctl Client struct
- Remove StreamDiff() method (never called)
- Remove CloseDiffStream() method
- Remove DiffUpdate type from client.go
- All diff data is already included in GitStatusUpdate.Files
- Keep server-side diff endpoint in agentctl for potential future use

* refactor: remove unused diff stream server-side code

- Remove /workspace/diff/stream endpoint from agentctl API
- Remove handleDiffStreamWS handler
- Remove DiffUpdate type from workspace_tracker.go
- Remove DiffSubscriber type
- Remove updateDiff() and getDiff() methods
- Remove SubscribeDiff(), UnsubscribeDiff() methods
- Remove notifyDiffSubscribers() method
- Remove GetCurrentDiff() method
- Remove currentDiff field and diffSubscribers map
- All diff data is already included in GitStatusUpdate.Files

* refactor: remove unused output stream code

- Remove /output and /output/stream endpoints from agentctl API
- Remove handleGetOutput and handleOutputStreamWS handlers
- Delete output.go file entirely
- Remove OutputBuffer and related code (buffer.go deleted)
- Remove outputConn field from agentctl Client
- Remove StreamOutput() and CloseOutputStream() methods
- Remove OutputLine type from client.go
- Remove OutputBufferSize config option
- Update readStderr to just log instead of buffering

Output data flows through ACP stream (StreamUpdates) which includes
all session notifications. The separate output stream was never used.

apps/backend/internal/task/repository/sqlite.go

@@ -757,6 +757,13 @@ func (r *SQLiteRepository) AddTaskToBoard(ctx context.Context, taskID, boardID,
 		VALUES (?, ?, ?, ?)
 		ON CONFLICT(task_id, board_id) DO UPDATE SET column_id = excluded.column_id, position = excluded.position
 	`, taskID, boardID, columnID, position)
+	if err != nil {
+		return err
+	}
+	// Also update the column_id in the tasks table so GetTask returns the correct column
+	_, err = r.db.ExecContext(ctx, `
+		UPDATE tasks SET column_id = ?, position = ?, updated_at = ? WHERE id = ?
+	`, columnID, position, time.Now().UTC(), taskID)
 	return err
 }
 
@@ -776,11 +783,18 @@ func (r *SQLiteRepository) addTaskToBoardTx(ctx context.Context, tx *sql.Tx, tas
 		return err
 	}
 
-	_, err := tx.ExecContext(ctx, `
+	if _, err := tx.ExecContext(ctx, `
 		INSERT INTO task_columns (task_id, board_id, column_id, position)
 		VALUES (?, ?, ?, ?)
 		ON CONFLICT(task_id, board_id) DO UPDATE SET column_id = excluded.column_id, position = excluded.position
-	`, taskID, boardID, columnID, position)
+	`, taskID, boardID, columnID, position); err != nil {
+		return err
+	}
+
+	// Also update the column_id in the tasks table so GetTask returns the correct column
+	_, err := tx.ExecContext(ctx, `
+		UPDATE tasks SET column_id = ?, position = ?, updated_at = ? WHERE id = ?
+	`, columnID, position, time.Now().UTC(), taskID)
 	return err
 }
 
@@ -914,6 +928,21 @@ func (r *SQLiteRepository) GetColumn(ctx context.Context, id string) (*models.Co
 	return column, err
 }
 
+// GetColumnByState retrieves a column by board ID and state
+func (r *SQLiteRepository) GetColumnByState(ctx context.Context, boardID string, state v1.TaskState) (*models.Column, error) {
+	column := &models.Column{}
+
+	err := r.db.QueryRowContext(ctx, `
+		SELECT id, board_id, name, position, state, color, created_at, updated_at
+		FROM columns WHERE board_id = ? AND state = ?
+	`, boardID, state).Scan(&column.ID, &column.BoardID, &column.Name, &column.Position, &column.State, &column.Color, &column.CreatedAt, &column.UpdatedAt)
+
+	if err == sql.ErrNoRows {
+		return nil, fmt.Errorf("column not found for board %s with state %s", boardID, state)
+	}
+	return column, err
+}
+
 // UpdateColumn updates an existing column
 func (r *SQLiteRepository) UpdateColumn(ctx context.Context, column *models.Column) error {
 	column.UpdatedAt = time.Now().UTC()