[DX] Bump `http-proxy-middleware@3`

[compulim]

Is your feature request related to a problem?

We did not bump http-proxy-middleware@3 in PR #5174.

Describe the suggestion or request in detail

• Remove http-proxy-middleware@2 from package.json/pinDependencies
• Run npm run bump to bump http-proxy-middleware
• Update our code so it works on http-proxy-middleware@3
  • Tests should run inside Docker without any timeout errors

Describe alternatives you have considered

No response

Additional context

No response