[CI] FullClusterRestartSystemIndexCompatibilityIT testAsyncSearchIndexMigration {p0=8.18.0} failing

[elasticsearchmachine]

Build Scans:

• elasticsearch-periodic-platform-support #8038 / windows-2022_checkpart1_platform-support-windows
• elasticsearch-periodic-platform-support #8032 / ubuntu-2404-aarch64_checkpart1_platform-support-arm
• elasticsearch-periodic-platform-support #8014 / ubuntu-2404-aarch64_checkpart1_platform-support-arm

Reproduction Line:

gradlew ":qa:lucene-index-compatibility:javaRestTest" --tests "org.elasticsearch.lucene.FullClusterRestartSystemIndexCompatibilityIT" -Dtests.method="testAsyncSearchIndexMigration {p0=8.18.0}" -Dtests.seed=AA972A430176EC91 -Dtests.locale=om-ET -Dtests.timezone=Africa/Bamako -Druntime.java=24

Applicable branches:
9.0

Reproduces locally?:
N/A

Failure History:
See dashboard

Failure Message:

java.lang.AssertionError: null

Issue Reasons:

• [9.0] 3 failures in test testAsyncSearchIndexMigration {p0=8.18.0} (2.8% fail rate in 107 executions)
• [9.0] 2 failures in step ubuntu-2404-aarch64_checkpart1_platform-support-arm (40.0% fail rate in 5 executions)
• [9.0] 3 failures in pipeline elasticsearch-periodic-platform-support (60.0% fail rate in 5 executions)

Note:
This issue was created using new test triage automation. Please report issues or feedback to es-delivery.

[elasticsearchmachine]

Pinging @elastic/es-search-foundations (Team:Search Foundations)

[cbuescher]

This test fails during an assertBusy while we're running against a 8.18 (or 8.19 lately) cluster waiting for an API call for migration of system indices to finish. The busy waiting block checks for the migration status to not be in "IN_PROGRESS" any longer but in the failure case fails after 10s. That seems ample time for that call to finish though (and most test runs finish in less than 1s as far as I have seen in local tests).
I'm going to add some logging to better see when we actually start migration and what the complete migration API output looks like in the failure case in #127710