Overlay by thrown error at initial load is closed immediately #5024

Bug report

Actual Behavior

Overlay by thrown error at initial load is closed immediately.

With debugger mode

Expected Behavior

Overlay by thrown error at initial load is not closed immediately.

How Do We Reproduce?

Just edit like below the photo to the overlay-example code. https://github.com/webpack/webpack-dev-server/blob/v4.15.1/examples/client/overlay/app.js#L49

Please paste the results of npx webpack-cli info here, and mention other relevant information

System:
  OS: macOS 13.4.1
  CPU: (10) arm64 Apple M1 Max
  Memory: 89.55 MB / 32.00 GB
Binaries:
  Node: 16.14.0 - ~/.nvm/versions/node/v16.14.0/bin/node
  Yarn: 3.6.4 - ~/.nvm/versions/node/v16.14.0/bin/yarn
  npm: 8.3.1 - ~/.nvm/versions/node/v16.14.0/bin/npm
Browsers:
  Chrome: 120.0.6099.109
  Safari: 16.5.2
Global Packages:
  webpack-dev-server: 4.15.1