feat(ui,docs): the open tab lives in the conversation url, admin screenshots in the readme

ui/src/lib/panel/conversation-view.svelte

@@ -18,6 +18,7 @@
     onOpen,
     showTitle = true,
     initialView = "chat",
+    onViewChange,
   }: {
     client: ApiClient;
     id: string;
@@ -27,6 +28,8 @@
     showTitle?: boolean;
     // "activity" beside a deep chat's own note: the file is the thread.
     initialView?: string;
+    // The page keeps the open tab in the URL so it survives a reload.
+    onViewChange?: (view: string) => void;
   } = $props();
 
   const host = usePanelHost();
@@ -50,6 +53,10 @@
     historyKey += 1;
   }
 
+  $effect(() => {
+    onViewChange?.(view);
+  });
+
   $effect(() => {
     const { running } = feed.model;
     if (!running) {

ui/src/routes/conversations/[id]/+page.svelte

@@ -1,5 +1,5 @@
 <script lang="ts">
-  import { goto } from "$app/navigation";
+  import { goto, replaceState } from "$app/navigation";
   import { base } from "$app/paths";
   import { page } from "$app/state";
   import ConversationView from "$lib/panel/conversation-view.svelte";
@@ -7,6 +7,22 @@
 
   const id = $derived(page.params.id ?? "");
   const href = (target: string) => `${base}/conversations/${target}`;
+
+  // ``?view=context`` opens that tab and stays in the address bar, so a
+  // reload (or a restart) lands where the reader was. Thread is the default
+  // and keeps the URL clean.
+  const initialView = $derived(page.url.searchParams.get("view") ?? "chat");
+  function remember(view: string) {
+    const url = new URL(page.url);
+    if (view === "chat") {
+      url.searchParams.delete("view");
+    } else {
+      url.searchParams.set("view", view);
+    }
+    if (url.href !== page.url.href) {
+      replaceState(url, page.state);
+    }
+  }
 </script>
 
 <svelte:head><title>Conversation · Beaver</title></svelte:head>
@@ -17,7 +33,9 @@
       client={session.client}
       {href}
       {id}
+      {initialView}
       onOpen={(target) => goto(href(target))}
+      onViewChange={remember}
     />
   {/key}
 {/if}