fix(webui): stabilize live thread rendering and navigation

webui/src/lib/tool-traces.ts

@@ -0,0 +1,30 @@
+export function formatToolCallTrace(call: unknown): string | null {
+  if (!call || typeof call !== "object") return null;
+  const item = call as {
+    name?: unknown;
+    arguments?: unknown;
+    function?: { name?: unknown; arguments?: unknown };
+  };
+  const name =
+    typeof item.function?.name === "string"
+      ? item.function.name
+      : typeof item.name === "string"
+        ? item.name
+        : "";
+  if (!name) return null;
+  const args = item.function?.arguments ?? item.arguments;
+  if (typeof args === "string" && args.trim()) return `${name}(${args})`;
+  if (args && typeof args === "object") return `${name}(${JSON.stringify(args)})`;
+  return `${name}()`;
+}
+
+export function toolTraceLinesFromEvents(events: unknown): string[] {
+  if (!Array.isArray(events)) return [];
+  return events
+    .filter((event) => {
+      if (!event || typeof event !== "object") return false;
+      return (event as { phase?: unknown }).phase === "start";
+    })
+    .map(formatToolCallTrace)
+    .filter((trace): trace is string => !!trace);
+}