I modified the function plot_dq_scatter_dropdown using the shapes argument instead of add_vline & add_hline arguments. Here is the revised function:

def plot_dq_scatter_dropdown(df):
# Initialize the figure
fig = go.Figure()

# Get columns for Y-axis options (excluding 'rows' and 'outlier_prob')
y_columns = [col for col in df.columns if col not in ["rows", "outlier_prob"]]
# Calculate median of rows (constant)
median_x = df["rows"].median()

# Create dropdown buttons with updated configuration
buttons = []
for y_col in y_columns:
    median_y = df[y_col].median()
    button = dict(
        label=y_col,
        method="update",
        args=[
            # Trace updates
            {
                "y": [df[y_col]],  # Update scatter plot Y values
                "x": [df["rows"]],
                "marker.color": [df["outlier_prob"]],
            },
            # Layout updates
            {
                "title": f"Scatter Plot: rows vs {y_col}",
                "yaxis.title": y_col,
                "shapes": [
                    # Vertical median line for rows
                    {
                        "type": "line",
                        "x0": median_x,
                        "x1": median_x,
                        "y0": 0,
                        "y1": 1,
                        "yref": "paper",
                        "line": {"color": "orange", "dash": "dash", "width": 2}
                    },
                    # Horizontal median line for selected Y variable
                    {
                        "type": "line",
                        "x0": 0,
                        "x1": 1,
                        "xref": "paper",
                        "y0": median_y,
                        "y1": median_y,
                        "line": {"color": "orange", "dash": "dash", "width": 2}
                    }
                ],
                "annotations": [
                    # Annotation for vertical median line
                    {
                        "x": median_x,
                        "y": 1,
                        "xref": "x",
                        "yref": "paper",
                        "text": "Median rows",
                        "showarrow": False,
                        "xanchor": "left",
                        "yanchor": "bottom"
                    },
                    # Annotation for horizontal median line
                    {
                        "x": 0,
                        "y": median_y,
                        "xref": "paper",
                        "yref": "y",
                        "text": f"Median {y_col}: {median_y:.2f}",
                        "showarrow": False,
                        "xanchor": "left",
                        "yanchor": "bottom"
                    }
                ]
            }
        ]
    )
    buttons.append(button)

# Add initial scatter plot
initial_y = y_columns[0]
initial_median_y = df[initial_y].median()
fig.add_trace(go.Scatter(
    x=df["rows"],
    y=df[initial_y],
    mode='markers',
    marker=dict(
        color=df['outlier_prob'],
        colorscale='viridis',
        showscale=True,
        colorbar=dict(title='Outlier Probability')
    ),
    hoverinfo='text',
    text=df.index,
    showlegend=False
))

# Update layout with dropdown menu and initial median lines
fig.update_layout(
    title=f"Scatter Plot: rows vs {initial_y}",
    xaxis_title="rows",
    yaxis_title=initial_y,
    updatemenus=[{
        "buttons": buttons,
        "direction": "down",
        "showactive": True,
        "x": 0.17,
        "y": 1.15,
        "type": "dropdown"
    }],
    shapes=[
        # Initial vertical median line
        {
            "type": "line",
            "x0": median_x,
            "x1": median_x,
            "y0": 0,
            "y1": 1,
            "yref": "paper",
            "line": {"color": "orange", "dash": "dash", "width": 2}
        },
        # Initial horizontal median line
        {
            "type": "line",
            "x0": 0,
            "x1": 1,
            "xref": "paper",
            "y0": initial_median_y,
            "y1": initial_median_y,
            "line": {"color": "orange", "dash": "dash", "width": 2}
        }
    ],
    annotations=[
        # Initial annotation for vertical median line
        {
            "x": median_x,
            "y": 1,
            "xref": "x",
            "yref": "paper",
            "text": "Median rows",
            "showarrow": False,
            "xanchor": "left",
            "yanchor": "bottom"
        },
        # Initial annotation for horizontal median line
        {
            "x": 0,
            "y": initial_median_y,
            "xref": "paper",
            "yref": "y",
            "text": f"Median {initial_y}: {initial_median_y:.2f}",
            "showarrow": False,
            "xanchor": "left",
            "yanchor": "bottom"
        }
    ]
)

# Show the plot
fig.show()

This should calculate the median values for each column and includes them in the button configuration. It also annotates the lines accordingly. I am attaching some images of the resulting output