Add model selection, dashboard chat input, and model warming

- Add GET /api/chat/ps and POST /api/chat/warm endpoints for hot model
  visibility and pre-loading
- Extend PATCH /api/chat/conversations/:id to accept model in addition
  to title
- Add ModelSelector component with hot/cold indicators from Ollama /api/ps
- Add DashboardChatInput component (model selector + note picker + textarea)
  replacing the simple "New Chat" button on the dashboard
- Add model selector dropdown to ChatView header, persisted per-conversation
- Warm default model on dashboard mount via fire-and-forget background task
- Configure Ollama with OLLAMA_MAX_LOADED_MODELS=2 and OLLAMA_KEEP_ALIVE=30m
- Always-visible edit buttons on NoteCard/TaskCard (remove hover-only behavior)

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

frontend/src/views/HomeView.vue

@@ -7,6 +7,7 @@ import type { Task, TaskListResponse } from "@/types/task";
 import type { Conversation } from "@/types/chat";
 import NoteCard from "@/components/NoteCard.vue";
 import TaskCard from "@/components/TaskCard.vue";
+import DashboardChatInput from "@/components/DashboardChatInput.vue";
 import type { TaskStatus } from "@/types/task";
 import { useTasksStore } from "@/stores/tasks";
 import { useChatStore } from "@/stores/chat";
@@ -166,11 +167,24 @@ function onStatusToggle(id: number, status: TaskStatus) {
   });
 }
 
-async function newChat() {
-  const chatStore = useChatStore();
-  const conv = await chatStore.createConversation();
+const chatStore = useChatStore();
+
+// Warm default model after status fetch
+chatStore.fetchStatus().then(() => {
+  if (chatStore.defaultModel) {
+    chatStore.warmModel(chatStore.defaultModel);
+  }
+});
+
+async function onChatSubmit(payload: {
+  content: string;
+  model: string;
+  contextNoteId?: number;
+}) {
+  const conv = await chatStore.createConversation("", payload.model);
   await chatStore.fetchConversation(conv.id);
   router.push(`/chat/${conv.id}`);
+  await chatStore.sendMessage(payload.content, payload.contextNoteId);
 }
 </script>
 
@@ -275,7 +289,7 @@ async function newChat() {
         <div v-else class="empty-state">
           <p class="empty-text">No chats yet.</p>
         </div>
-        <button class="btn-cta btn-new-chat" @click="newChat">+ New Chat</button>
+        <DashboardChatInput @submit="onChatSubmit" />
       </section>
 
       <section class="section">
@@ -374,9 +388,6 @@ async function newChat() {
   color: var(--color-text-muted);
   white-space: nowrap;
 }
-.btn-new-chat {
-  margin-top: 0.75rem;
-}
 .empty-state {
   text-align: center;
   padding: 1.5rem 0;