Run e2e test with a binary built with `-race` flag

*Description*:

I have discovered quite a few race conditions around the main routine of `envoy-gateway` program #5538 #5505 #5522 in the last few days, and I believe there are still more to be discovered due to the lack of the test around the main program.

Critical orchestration of many goroutines happens in the main routine, so I believe this is really important to make this project more robust.

I recommend that we write comprehensive main program unit tests for all the EG configuration (not partially like i did in AI Gateway but this must include Kubernetes provider) or run e2e/integration tests with the binary built with `-race`, which I think is easier to test k8s provider.