How to get webpack-dev-server to work properly and set proxy in browsersync?

Question

proxy

Greetings! There are 2 questions.
1. Using webpack-dev-server, I noticed that on some projects it crashes and fills up the console

mistakes

2. I tried to switch to browsersync, but it did not work to configure the proxy in the same way as in webpack-dev-server.
Test project repository . Command "npm run wds" to run web-dev-server on localhost:8080, "npm run dev" to run browsersync on localhost:3000.