test: wait for readiness instead of sleeping in TestTrivialERS

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Description

I inspected the latest successful main runs for both unit_test.yml and cluster_endtoend.yml in vitessio/vitess and found the cluster workflow was the real wall-clock bottleneck. In run 23057103687, the slowest job was ers_prs_newfeatures_heavy at about 24m17s, noticeably slower than any job in the latest successful unit-test run.

Within that shard, go/test/endtoend/reparent/emergencyreparent was a major contributor at about 8m21s, and TestTrivialERS alone took about 62.97s. The biggest avoidable cost in that test was eight unconditional time.Sleep(5 * time.Second) calls between repeated ERS invocations.

This PR replaces those fixed sleeps with a readiness check that waits for:

• exactly one healthy primary,
• a valid topology state, and
• working replication to all replicas.

That keeps the same end-to-end assertion intact — repeated ERS operations must leave the shard healthy and replicating — while removing idle wait time.

I also checked open PRs before making this change. I did not find an open PR already addressing TestTrivialERS or the ers_prs_newfeatures_heavy shard specifically; the closest related open PR I saw was #19622, which focuses on e2e teardown/orphaned processes rather than this test’s fixed waits.

Local validation:

• go test -count=1 -timeout 15m -run '^TestTrivialERS$' vitess.io/vitess/go/test/endtoend/reparent/emergencyreparent
  • before: 61.383s
  • after: 31.282s
• go test -count=1 -timeout 25m vitess.io/vitess/go/test/endtoend/reparent/emergencyreparent
  • after: 453.887s (7m33.887s)
  • reference CI package time from the inspected run: about 8m21.062s

Related Issue(s)

None.

Checklist

• "Backport to:" labels have been added if this change should be back-ported to release branches
• If this change is to be back-ported to previous releases, a justification is included in the PR description
• Tests were added or are not required
• Did the new or modified tests pass consistently locally and on CI?
• Documentation was added or is not required

Deployment Notes

None.

AI Disclosure

This PR was written primarily by GPT-5.