[E2E Framework] Improve E2E Framework to Collect Debug Artifacts on clusterctl init Failures

What would you like to be added (User Story)?

As a developer, I would like to access the debug info in artifacts on clusterctl init failures.

Detailed Description

Currently, when running E2E tests, if clusterctl init fails (e.g., due to CAPI components not reaching a Ready status as below), the test artifacts do not contain sufficient information to debug. This lack of context makes it difficult to identify root causes especially when we couldn't access infra.

We need e2eframework to collect the relevant diagnostic data when clusterctl init or early cluster bootstrap steps fail.

INFO: The kubeconfig file for the kind cluster is /tmp/e2e-kind3738542185
  STEP: Initialize bootstrap cluster @ 05/07/25 06:16:33.625
  INFO: clusterctl init --config /tmp/tmp.I8vcxeUaCN/repository/clusterctl-config.yaml --kubeconfig /tmp/e2e-kind3738542185 --wait-providers --core cluster-api --bootstrap kubeadm --control-plane kubeadm --infrastructure vsphere
  [FAILED] in [SynchronizedBeforeSuite] - /home/prow/go/pkg/mod/sigs.k8s.io/cluster-api/test@v1.10.1/framework/clusterctl/client.go:90 @ 05/07/25 06:22:18.911
[SynchronizedBeforeSuite] [FAILED] [396.063 seconds]
[SynchronizedBeforeSuite] 
/home/prow/go/src/k8s.io/cloud-provider-vsphere/test/e2e/e2e_suite_test.go:143
  [FAILED] failed to run clusterctl init
  Unexpected error:
      <*errors.withStack | 0xc0000108e8>: 
      deployment "capi-controller-manager" is not ready after 5m0s: context deadline exceeded
      {
          error: <*errors.withMessage | 0xc0022e6680>{
              cause: <context.deadlineExceededError>{},
              msg: "deployment \"capi-controller-manager\" is not ready after 5m0s",
          },
          stack: [0x24b[807](http://52.34.10.152:30002/view/s3/prow-logs/pr-logs/pull/team-cluster-api_cloud-provider-vsphere/89/pull-cloud-provider-vsphere-e2e-test/1919998318331564032#1:build-log.txt%3A807)0, 0x24b7da7, 0x24b74b4, 0x24fa1ce, 0x259ce8a, 0x259f64b, 0x264e3f3, 0x19aa3a2, 0x19bae16, 0x264d479, 0x5029c6, 0x501ad9, 0x199eede, 0x19af1ce, 0x19b29fb, 0x4841a1],
      }
  occurred
  In [SynchronizedBeforeSuite] at: /home/prow/go/pkg/mod/sigs.k8s.io/cluster-api/test@v1.10.1/framework/clusterctl/client.go:90 @ 05/07/25 06:22:18.911

Anything else you would like to add?

No response

Label(s) to be applied

/kind feature One or more /area label. See https://github.com/kubernetes-sigs/cluster-api/labels?q=area for the list of labels.