feat: implement Story 3.1 — chat panel UI with streaming AI responses

Add AI copilot chat panel to the diagram editor with streaming responses,
chat history persistence, and markdown rendering. Includes copilot API route,
diagram-aware system prompt, and schema with 15 passing tests.

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

packages/db/migrations/0002_numerous_siren.sql

@@ -0,0 +1,2 @@
+ALTER TABLE "chat"."chat" ADD COLUMN "diagram_id" text;--> statement-breakpoint
+CREATE INDEX "chat_diagram_id_idx" ON "chat"."chat" USING btree ("diagram_id");

packages/db/migrations/meta/_journal.json

@@ -15,6 +15,13 @@
       "when": 1771885601062,
       "tag": "0001_fuzzy_gorilla_man",
       "breakpoints": true
+    },
+    {
+      "idx": 2,
+      "version": "7",
+      "when": 1772245471347,
+      "tag": "0002_numerous_siren",
+      "breakpoints": true
     }
   ]
 }

packages/db/src/schema/chat.ts

@@ -1,5 +1,12 @@
 import { relations } from "drizzle-orm";
-import { integer, jsonb, pgSchema, timestamp, text } from "drizzle-orm/pg-core";
+import {
+  index,
+  integer,
+  jsonb,
+  pgSchema,
+  timestamp,
+  text,
+} from "drizzle-orm/pg-core";
 
 import { generateId } from "@turbostarter/shared/utils";
 
@@ -15,17 +22,22 @@ export const messageRoleEnum = schema.enum("role", [
   "user",
 ]);
 
-export const chat = schema.table("chat", {
-  id: text().primaryKey().notNull().$defaultFn(generateId),
-  name: text(),
-  userId: text()
-    .references(() => user.id, {
-      onDelete: "cascade",
-      onUpdate: "cascade",
-    })
-    .notNull(),
-  createdAt: timestamp().defaultNow(),
-});
+export const chat = schema.table(
+  "chat",
+  {
+    id: text().primaryKey().notNull().$defaultFn(generateId),
+    name: text(),
+    diagramId: text(),
+    userId: text()
+      .references(() => user.id, {
+        onDelete: "cascade",
+        onUpdate: "cascade",
+      })
+      .notNull(),
+    createdAt: timestamp().defaultNow(),
+  },
+  (t) => [index("chat_diagram_id_idx").on(t.diagramId)],
+);
 
 export const message = schema.table("message", {
   id: text().primaryKey().notNull().$defaultFn(generateId),