[Integration Test Failures] Tracking bug

[elliette]

Some of our integration tests have suddenly begun failing. This is a tracking bug for the investigation and fixes.

Possibly related to Chrome / ChromeDriver update, since no changes have been made in DevTools.

Successful run

• https://github.com/flutter/devtools/actions/runs/21402249586/job/61616639862
• logs_55563736520.zip

Unsuccessful run

• https://github.com/flutter/devtools/actions/runs/21527631142/job/62035399292?pr=9638
• logs_55943496892.zip