fix(db): rename pgSchema exports to prevent barrel collision

chat/image/mesh modules all exported a generic `const schema`
binding. When packages/db/src/schema/index.ts did `export * from
"./chat"` + `export * from "./image"` + `export * from "./mesh"`,
TypeScript's ambiguous-re-export rule silently dropped the colliding
bindings — drizzle-kit's introspection could not find the pgSchema
instances, so CREATE SCHEMA statements were never emitted. The
migration worked on the prior dev DB only because chat/image already
existed from an earlier turbostarter run; a fresh clone would fail.

pdf.ts already used `pdfSchema` (unique name). Applied the same
pattern everywhere:
- chat.ts:  `export const chatSchema = pgSchema("chat")`
- image.ts: `export const imageSchema = pgSchema("image")`
- mesh.ts:  `export const meshSchema = pgSchema("mesh")`

Also added `CREATE EXTENSION IF NOT EXISTS vector` at the top of the
migration (pgvector is used by pdf.embedding — the generated
migration assumed it was pre-enabled).

Verified end-to-end against a fresh pgvector/pgvector:pg17 container:
`pnpm drizzle-kit migrate` applies cleanly from scratch, all 7 mesh.*
tables + chat/image/pdf/mesh schemas created correctly.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

packages/db/src/schema/chat.ts

@@ -7,15 +7,18 @@ import { createInsertSchema, createSelectSchema } from "../utils/drizzle-zod";
 
 import { user } from "./auth";
 
-export const schema = pgSchema("chat");
+// Uniquely-named pgSchema export (not `schema`) so drizzle-kit can
+// introspect it through the `export * from "./chat"` barrel. See
+// mesh.ts for the full rationale.
+export const chatSchema = pgSchema("chat");
 
-export const messageRoleEnum = schema.enum("role", [
+export const messageRoleEnum = chatSchema.enum("role", [
   "system",
   "assistant",
   "user",
 ]);
 
-export const chat = schema.table("chat", {
+export const chat = chatSchema.table("chat", {
   id: text().primaryKey().notNull().$defaultFn(generateId),
   name: text(),
   userId: text()
@@ -27,7 +30,7 @@ export const chat = schema.table("chat", {
   createdAt: timestamp().defaultNow(),
 });
 
-export const message = schema.table("message", {
+export const message = chatSchema.table("message", {
   id: text().primaryKey().notNull().$defaultFn(generateId),
   chatId: text()
     .references(() => chat.id, { onDelete: "cascade", onUpdate: "cascade" })
@@ -40,7 +43,7 @@ export const messageRelations = relations(message, ({ many }) => ({
   part: many(part),
 }));
 
-export const part = schema.table("part", {
+export const part = chatSchema.table("part", {
   id: text().primaryKey().notNull().$defaultFn(generateId),
   messageId: text()
     .references(() => message.id, { onDelete: "cascade", onUpdate: "cascade" })