feat: add icicle chart rendering with NHS colorscale and dynamic titles (Task 3.4)

- Add create_icicle_from_nodes() to src/visualization/plotly_generator.py
  accepting list-of-dicts from dcc.Store with NHS blue gradient colorscale,
  10-field customdata, and matching text/hover templates from Reflex version
- Add update_chart callback to dash_app/callbacks/chart.py rendering
  go.Icicle figure from chart-data store with dynamic subtitle
- Title generation helper mirrors Reflex _generate_pathway_chart_title()

src/visualization/plotly_generator.py

@@ -110,6 +110,140 @@ def create_icicle_figure(ice_df: pd.DataFrame, title: str) -> go.Figure:
     return fig
 
 
+def create_icicle_from_nodes(nodes: list[dict], title: str = "") -> go.Figure:
+    """
+    Create Plotly icicle figure from a list of pathway node dicts.
+
+    This is the dict-based entry point used by the Dash app. The nodes list
+    comes directly from the chart-data dcc.Store (JSON-serialized dicts with
+    underscore keys matching SQLite column names).
+
+    Args:
+        nodes: List of dicts with keys: parents, ids, labels, value, cost,
+               costpp, cost_pp_pa, colour, first_seen, last_seen,
+               first_seen_parent, last_seen_parent, average_spacing
+        title: Chart title (e.g. "By Directory | All years / Last 6 months")
+
+    Returns:
+        Plotly Figure object ready for dcc.Graph
+    """
+    if not nodes:
+        return go.Figure()
+
+    parents = [d.get("parents", "") for d in nodes]
+    ids = [d.get("ids", "") for d in nodes]
+    labels = [d.get("labels", "") for d in nodes]
+    values = [d.get("value", 0) for d in nodes]
+    colours = [d.get("colour", 0.0) for d in nodes]
+
+    costs = [d.get("cost", 0.0) for d in nodes]
+    costpp = [d.get("costpp", 0.0) for d in nodes]
+    first_seen = [d.get("first_seen", "N/A") or "N/A" for d in nodes]
+    last_seen = [d.get("last_seen", "N/A") or "N/A" for d in nodes]
+    first_seen_parent = [d.get("first_seen_parent", "N/A") or "N/A" for d in nodes]
+    last_seen_parent = [d.get("last_seen_parent", "N/A") or "N/A" for d in nodes]
+    average_spacing = [d.get("average_spacing", "") or "" for d in nodes]
+    cost_pp_pa = [d.get("cost_pp_pa", 0.0) or 0.0 for d in nodes]
+
+    customdata = list(zip(
+        values,              # [0]
+        colours,             # [1]
+        costs,               # [2]
+        costpp,              # [3]
+        first_seen,          # [4]
+        last_seen,           # [5]
+        first_seen_parent,   # [6]
+        last_seen_parent,    # [7]
+        average_spacing,     # [8]
+        cost_pp_pa,          # [9]
+    ))
+
+    # NHS blue gradient (Heritage Blue → Primary Blue → Vibrant Blue → Sky Blue → Pale Blue)
+    colorscale = [
+        [0.0, "#003087"],
+        [0.25, "#0066CC"],
+        [0.5, "#1E88E5"],
+        [0.75, "#4FC3F7"],
+        [1.0, "#E3F2FD"],
+    ]
+
+    fig = go.Figure(
+        go.Icicle(
+            labels=labels,
+            ids=ids,
+            parents=parents,
+            values=values,
+            branchvalues="total",
+            marker=dict(
+                colors=colours,
+                colorscale=colorscale,
+                line=dict(width=1, color="#FFFFFF"),
+            ),
+            maxdepth=3,
+            customdata=customdata,
+            texttemplate=(
+                "<b>%{label}</b> "
+                "<br><b>Total patients:</b> %{customdata[0]} (including children/further treatments)"
+                "<br><b>First seen:</b> %{customdata[4]}"
+                "<br><b>Last seen (including further treatments):</b> %{customdata[7]}"
+                "<br><b>Average treatment duration:</b> %{customdata[8]}"
+                "<br><b>Total cost:</b> \u00a3%{customdata[2]:.3~s}"
+                "<br><b>Average cost per patient:</b> \u00a3%{customdata[3]:.3~s}"
+                "<br><b>Average cost per patient per annum:</b> \u00a3%{customdata[9]:.3~s}"
+            ),
+            hovertemplate=(
+                "<b>%{label}</b>"
+                "<br><b>Total patients:</b> %{customdata[0]} - %{customdata[1]:.3p} of patients in level"
+                "<br><b>Total cost:</b> \u00a3%{customdata[2]:.3~s}"
+                "<br><b>Average cost per patient:</b> \u00a3%{customdata[3]:.3~s}"
+                "<br><b>Average cost per patient per annum:</b> \u00a3%{customdata[9]:.3~s}"
+                "<br><b>First seen:</b> %{customdata[4]}"
+                "<br><b>Last seen (including further treatments):</b> %{customdata[7]}"
+                "<br><b>Average treatment duration:</b>"
+                "%{customdata[8]}"
+                "<extra></extra>"
+            ),
+            textfont=dict(
+                family="Source Sans 3, system-ui, sans-serif",
+                size=12,
+            ),
+        )
+    )
+
+    display_title = f"Patient Pathways \u2014 {title}" if title else "Patient Pathways"
+
+    fig.update_layout(
+        title=dict(
+            text=display_title,
+            font=dict(
+                family="Source Sans 3, system-ui, sans-serif",
+                size=18,
+                color="#1E293B",
+            ),
+            x=0.5,
+            xanchor="center",
+        ),
+        margin=dict(t=40, l=8, r=8, b=24),
+        hoverlabel=dict(
+            bgcolor="#FFFFFF",
+            bordercolor="#CBD5E1",
+            font=dict(
+                family="Source Sans 3, system-ui, sans-serif",
+                size=14,
+                color="#1E293B",
+            ),
+        ),
+        paper_bgcolor="rgba(0,0,0,0)",
+        plot_bgcolor="rgba(0,0,0,0)",
+        autosize=True,
+        clickmode="event+select",
+    )
+
+    fig.update_traces(sort=False)
+
+    return fig
+
+
 def save_figure_html(
     fig: go.Figure, save_dir: str, title: str, open_browser: bool = False
 ) -> str: