[code-infra] Port integration tests to pigment repository

[Janpot]

https://github.com/mui/material-ui/tree/master/apps

To free up the core team from having to maintain these. Currently they directly import from the docs. This creates tech debt in a sense that

• This wasn't built in the existing regression tests suite, so code-infra needs to maintain two regression test suites
• It directly imports docs, so now core maintainers will need to keep the test suite up to date as the docs evolve

We should move this to the pigment repository