perf(dashboard): optimize random book lookups and scroller batching

Add index on books table for random dashboard scroller queries, batch dashboard scroller requests, instrument pg pool logging, and cover dashboard scroller batching in e2e tests.

client/vite.config.ts

@@ -1,4 +1,5 @@
 import { fileURLToPath, URL } from 'node:url'
+import { Agent } from 'node:http'
 
 import { defineConfig } from 'vite'
 import vue from '@vitejs/plugin-vue'
@@ -6,6 +7,8 @@ import vueDevTools from 'vite-plugin-vue-devtools'
 import tailwindcss from '@tailwindcss/vite'
 import { VitePWA } from 'vite-plugin-pwa'
 
+const apiAgent = new Agent({ keepAlive: true })
+
 // https://vite.dev/config/
 export default defineConfig({
   define: {
@@ -141,6 +144,7 @@ export default defineConfig({
     proxy: {
       '/api': {
         target: 'http://localhost:3000',
+        agent: apiAgent,
         configure: (proxy) => {
           proxy.on('proxyReq', (proxyReq, req) => {
             if (req.headers.host) proxyReq.setHeader('x-forwarded-host', req.headers.host)