feat(sidebar B.1 #31): visible LLM status chip with live state

The LLM runtime has been quiet since it shipped in Phase 3 — users
had no surface-level signal that cleanup was loaded, warming, or
actively generating. Settings has verbose status text internally,
but a dictation-flow user never opens Settings during a run.

New: a shared $state store drives a small chip in the sidebar that
reflects the true LLM state in ≤500 ms of any transition (brief
item #31 acceptance). Five states:

  off        → hidden (user has aiTier === "off")
  warming    → model download or first load in flight; amber pulse
  ready      → loaded + idle; green dot
  generating → cleanup_transcript_text_cmd or
               extract_tasks_from_transcript_cmd in flight; accent
               pulse with Sparkles icon
  error      → last operation failed; red dot with AlertTriangle

The store exposes three calls: refreshLlmStatus(aiTier) (polls the
backend), markGenerating(detail) / markGenerationDone(success).
DictationPage wraps its cleanup + extract calls in mark-generating
pairs. SettingsPage's LLM load / unload / delete / download paths
also refresh the global store so Settings-initiated transitions
surface in the sidebar immediately. The chip collapses to a
dot-only compact form when the sidebar is collapsed.

No backend changes — everything wires onto the existing
`get_llm_status` Tauri command.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

src/lib/Sidebar.svelte

@@ -1,6 +1,7 @@
 <script lang="ts">
   import { page, settings, tasks, saveSettings } from "$lib/stores/page.svelte.js";
   import { Mic, FileText, SquareCheck, Clock, Settings, ChevronRight, ChevronLeft } from 'lucide-svelte';
+  import LlmStatusChip from "$lib/components/LlmStatusChip.svelte";
 
   let taskCount = $derived(tasks.filter((t) => !t.done).length);
 
@@ -53,6 +54,17 @@
 
   {#if !collapsed}
     <p class="text-[10px] text-text-tertiary px-5 mt-1.5 tracking-[0.12em] uppercase">Think out loud</p>
+    <!-- LLM status chip — hidden when aiTier === off, otherwise reflects
+         disconnected / warming / ready / generating / error state live. -->
+    <div class="px-5 mt-2">
+      <LlmStatusChip />
+    </div>
+  {:else}
+    <!-- Collapsed: compact dot-only chip so the sidebar still surfaces
+         the state without eating horizontal space. -->
+    <div class="mt-2 flex justify-center">
+      <LlmStatusChip compact />
+    </div>
   {/if}
 
   <!-- Separator -->