Bump engine.io and browser-sync in /client

Bumps [engine.io](https://github.com/socketio/engine.io) to 6.2.1 and updates ancestor dependency [browser-sync](https://github.com/BrowserSync/browser-sync). These dependencies need to be updated together.


Updates `engine.io` from 3.5.0 to 6.2.1
- [Release notes](https://github.com/socketio/engine.io/releases)
- [Changelog](https://github.com/socketio/engine.io/blob/main/CHANGELOG.md)
- [Commits](https://github.com/socketio/engine.io/compare/3.5.0...6.2.1)

Updates `browser-sync` from 2.27.5 to 2.27.10
- [Release notes](https://github.com/BrowserSync/browser-sync/releases)
- [Changelog](https://github.com/BrowserSync/browser-sync/blob/master/CHANGELOG.md)
- [Commits](https://github.com/BrowserSync/browser-sync/compare/v2.27.5...v2.27.10)

---
updated-dependencies:
- dependency-name: engine.io
  dependency-type: indirect
- dependency-name: browser-sync
  dependency-type: direct:development
...

Signed-off-by: dependabot[bot] <support@github.com>

client/package.json

@@ -30,7 +30,7 @@
     "axios-mock-adapter": "^1.15.0",
     "babel-loader": "^8.0.6",
     "babel-plugin-add-module-exports": "^1.0.2",
-    "browser-sync": "^2.27.5",
+    "browser-sync": "^2.27.10",
     "chai": "^3.5.0",
     "copy-webpack-plugin": "^5.0.3",
     "css-loader": "^3.0.0",