Bring the end-to-end environment up faster #868

Both end-to-end workflows bring up the same environment with task test-infra:up, and it took 10 to 11 minutes of every green run on main between 2026-11-04 15:04Z and 2026-11-05 10:02Z, for example in E2E Tests and Federated E2E. Its tasks run one after another.

Two of its longest tasks wait without need, as the logs of three of those runs show.

Proposed scope

• Keep the Go module and build caches between runs: cache mounts in the Dockerfile, with the cache kept in GitHub Actions' cache, as Optimize PR E2E foundation bootstrap, shared builds and caches dns-operator#433 does.
• Build the image while the clusters come up.
• Start Karmada beside the Milo and IPAM tasks.
• Measure the three changes together on repeated runs. Parallel work on one runner adds resource pressure, which is one reason the suite runs one test at a time.

Non-goals

• The suite's own time. It has its own issue under the same Epic.
• What the published image contains. The release builds from the same Dockerfile, so the cache mounts must not change its output.
• Self-hosted runners.

Acceptance criteria

• On repeated runs on main, the bring-up takes less than 10 minutes in both end-to-end workflows.
• A run with an empty cache takes no longer than the runs above.
• The published image holds the same files as before.