fix: storefront live search relative URLs + auth error messages + TPV clock

- Storefront: use relative URLs in api.ts (fix ERR_ADDRESS_UNREACHABLE)
- Auth: show specific error for EMAIL_NOT_CONFIRMED
- TPV: add clock with date/time, modern SVG icons, panel toggle left

project/src/modules/inventory/api/inventory.routes.ts

@@ -22,6 +22,7 @@ export interface InventoryRoutesDeps {
 }
 
 const variantParamSchema = z.object({ variantId: z.uuid() });
+const productParamSchema = z.object({ productId: z.uuid() });
 const availabilityQuerySchema = z.object({
   quantity: z.coerce.number().int().positive().default(1),
   storeId: z.uuid().optional(),
@@ -80,6 +81,49 @@ export async function registerInventoryRoutes(
     },
   );
 
+  // GET /inventory/product/:productId/availability — lookup first variant and return stock
+  const productAvailabilitySchema: FastifySchema = {
+    tags: ['Inventory'],
+    summary: 'Check availability by productId (público)',
+    params: {
+      type: 'object',
+      required: ['productId'],
+      properties: { productId: { type: 'string', format: 'uuid' } },
+    },
+    querystring: {
+      type: 'object',
+      properties: {
+        quantity: { type: 'integer', default: 1 },
+        storeId: { type: 'string', format: 'uuid' },
+      },
+    },
+  };
+  app.get(
+    '/inventory/product/:productId/availability',
+    { schema: productAvailabilitySchema },
+    async (request, reply) => {
+      const { productId } = parseJson(productParamSchema, request.params);
+      const { quantity, storeId } = parseJson(availabilityQuerySchema, request.query);
+
+      // Lookup the first variant for this product
+      const variantResult = await deps.pool.query(
+        `SELECT id FROM product_variants WHERE product_id = $1 LIMIT 1`,
+        [productId],
+      );
+      if (variantResult.rows.length === 0) {
+        throw new AppError(404, 'VARIANT_NOT_FOUND', 'No variant found for this product');
+      }
+      const variantId = variantResult.rows[0].id;
+
+      const availability = await inventory.checkAvailability(
+        variantId,
+        storeId ?? DEFAULT_STORE_ID,
+        quantity,
+      );
+      return reply.send(availability);
+    },
+  );
+
   const setStockSchema: FastifySchema = {
     tags: ['Inventory'],
     summary: 'Set available stock (admin)',