Source GitHub: use airbytehq/integration-test repo for tests instead of airbytehq/airbyte

[Zirochkaa]

Tell us about the problem you're trying to solve

Currently GitHub connector uses airbytehq/airbyte repo for tests. It eat up a lot of requests (a few thousand requests per each test run) and it's slow. In #4750 and #5674 repo for tests was created and filled with data. Now we need to use it in tests.

Describe the solution you’d like

Update config with new repo and maybe update test files with state.

Describe the alternative you’ve considered or used

Just live with slow tests and tons of requests ;(

Additional context

Nope.

Are you willing to submit a PR?

Yes.