Add sync error logging, extend error flash, fix unload saves

- Log workforce sync errors to backend stdout so they appear in docker logs
- Extend error flash from 5s to 15s so errors are readable
- Replace sendBeacon (POST-only) with keepalive fetch (PUT) on unload —
  sendBeacon was hitting 404s on all three unload saves

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

frontend/node_modules/fs-extra/lib/path-exists/index.js

@@ -0,0 +1,12 @@
+'use strict'
+const u = require('universalify').fromPromise
+const fs = require('../fs')
+
+function pathExists (path) {
+  return fs.access(path).then(() => true).catch(() => false)
+}
+
+module.exports = {
+  pathExists: u(pathExists),
+  pathExistsSync: fs.existsSync
+}