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/pages/SettingsPage.svelte

@@ -18,6 +18,10 @@
   import { Check, ChevronRight } from "lucide-svelte";
   import { _ } from "svelte-i18n";
   import { SUPPORTED_LOCALES, setLocale, currentLocale } from "$lib/i18n";
+  // Aliased because SettingsPage has its own local refreshLlmStatus
+  // that just mutates the page-local llmLoaded bool. The store
+  // version drives the sidebar chip (brief item #31).
+  import { refreshLlmStatus as refreshGlobalLlmStatus } from "$lib/stores/llmStatus.svelte.js";
 
   const prefs = getPreferences();
 
@@ -515,6 +519,7 @@
       await invoke("download_llm_model", { modelId });
       llmDownloadingModel = "";
       await refreshLlmStatus();
+      await refreshGlobalLlmStatus(settings.aiTier);
       llmStatus = "Download complete";
     } catch (err) {
       llmDownloadingModel = "";
@@ -528,6 +533,7 @@
     try {
       await invoke("load_llm_model", { modelId });
       await refreshLlmStatus();
+      await refreshGlobalLlmStatus(settings.aiTier);
     } catch (err) {
       llmStatus = typeof err === "string" ? err : "LLM load failed";
     }
@@ -537,6 +543,7 @@
     try {
       await invoke("unload_llm_model");
       await refreshLlmStatus();
+      await refreshGlobalLlmStatus(settings.aiTier);
       llmStatus = "Model unloaded";
     } catch (err) {
       llmStatus = typeof err === "string" ? err : "LLM unload failed";
@@ -548,6 +555,7 @@
     try {
       await invoke("delete_llm_model", { modelId });
       await refreshLlmStatus();
+      await refreshGlobalLlmStatus(settings.aiTier);
       llmStatus = "Downloaded model removed";
     } catch (err) {
       llmStatus = typeof err === "string" ? err : "Delete failed";
@@ -574,6 +582,7 @@
       await unloadLlmModel();
     } else {
       await refreshLlmStatus();
+      await refreshGlobalLlmStatus(settings.aiTier);
     }
     llmStatus = llmModelDownloaded(modelId)
       ? "Selected model changed. Load it to enable AI features."
@@ -585,6 +594,7 @@
     if (openSection === 'ai') {
       await ensureRecommendedLlmTier();
       await refreshLlmStatus();
+      await refreshGlobalLlmStatus(settings.aiTier);
     }
   }
 
@@ -594,6 +604,7 @@
       systemInfo = await invoke("probe_system").catch(() => null);
       await ensureRecommendedLlmTier();
       await refreshLlmStatus();
+      await refreshGlobalLlmStatus(settings.aiTier);
       const loaded = await invoke("check_engine");
       engineOk = loaded;
       engineStatus = loaded ? "Model loaded" : "No model loaded";