ui(chat): persist session in URL and stabilize picker

- Keep the selected chat session in ?session=... for deep links and reloads.\n- Only apply the query param on the Chat tab (avoid leaking it across navigation).\n- Render session <option> entries with stable keys to prevent label glitches.

ui/src/ui/app-render.helpers.ts

@@ -1,8 +1,10 @@
 import { html } from "lit";
+import { repeat } from "lit/directives/repeat.js";
 
 import type { AppViewState } from "./app-view-state";
 import { iconForTab, pathForTab, titleForTab, type Tab } from "./navigation";
 import { loadChatHistory } from "./controllers/chat";
+import { syncUrlWithSessionKey } from "./app-settings";
 import type { SessionsListResult } from "./types";
 import type { ThemeMode } from "./theme";
 import type { ThemeTransitionContext } from "./theme-transition";
@@ -64,10 +66,13 @@ export function renderChatControls(state: AppViewState) {
               sessionKey: next,
               lastActiveSessionKey: next,
             });
+            syncUrlWithSessionKey(state, next, true);
             void loadChatHistory(state);
           }}
         >
-          ${sessionOptions.map(
+          ${repeat(
+            sessionOptions,
+            (entry) => entry.key,
             (entry) =>
               html`<option value=${entry.key}>
                 ${entry.displayName ?? entry.key}
@@ -119,9 +124,11 @@ function resolveSessionOptions(sessionKey: string, sessions: SessionsListResult
   const seen = new Set<string>();
   const options: Array<{ key: string; displayName?: string }> = [];
 
+  const resolvedCurrent = sessions?.sessions?.find((s) => s.key === sessionKey);
+
   // Add current session key first
   seen.add(sessionKey);
-  options.push({ key: sessionKey });
+  options.push({ key: sessionKey, displayName: resolvedCurrent?.displayName });
 
   // Add sessions from the result
   if (sessions?.sessions) {

ui/src/ui/app-settings.ts

@@ -85,9 +85,12 @@ export function applySettingsFromUrl(host: SettingsHost) {
     const session = sessionRaw.trim();
     if (session) {
       host.sessionKey = session;
+      applySettings(host, {
+        ...host.settings,
+        sessionKey: session,
+        lastActiveSessionKey: session,
+      });
     }
-    params.delete("session");
-    shouldCleanUrl = true;
   }
 
   if (!shouldCleanUrl) return;
@@ -225,6 +228,18 @@ export function onPopState(host: SettingsHost) {
   if (typeof window === "undefined") return;
   const resolved = tabFromPath(window.location.pathname, host.basePath);
   if (!resolved) return;
+
+  const url = new URL(window.location.href);
+  const session = url.searchParams.get("session")?.trim();
+  if (session) {
+    host.sessionKey = session;
+    applySettings(host, {
+      ...host.settings,
+      sessionKey: session,
+      lastActiveSessionKey: session,
+    });
+  }
+
   setTabFromRoute(host, resolved);
 }
 
@@ -241,9 +256,18 @@ export function syncUrlWithTab(host: SettingsHost, tab: Tab, replace: boolean) {
   if (typeof window === "undefined") return;
   const targetPath = normalizePath(pathForTab(tab, host.basePath));
   const currentPath = normalizePath(window.location.pathname);
-  if (currentPath === targetPath) return;
   const url = new URL(window.location.href);
-  url.pathname = targetPath;
+
+  if (tab === "chat" && host.sessionKey) {
+    url.searchParams.set("session", host.sessionKey);
+  } else {
+    url.searchParams.delete("session");
+  }
+
+  if (currentPath !== targetPath) {
+    url.pathname = targetPath;
+  }
+
   if (replace) {
     window.history.replaceState({}, "", url.toString());
   } else {
@@ -251,6 +275,18 @@ export function syncUrlWithTab(host: SettingsHost, tab: Tab, replace: boolean) {
   }
 }
 
+export function syncUrlWithSessionKey(
+  host: SettingsHost,
+  sessionKey: string,
+  replace: boolean,
+) {
+  if (typeof window === "undefined") return;
+  const url = new URL(window.location.href);
+  url.searchParams.set("session", sessionKey);
+  if (replace) window.history.replaceState({}, "", url.toString());
+  else window.history.pushState({}, "", url.toString());
+}
+
 export async function loadOverview(host: SettingsHost) {
   await Promise.all([
     loadChannels(host as unknown as ClawdbotApp, false),