Fix flaky Docker integration tests

What does this MR do?

Previously Test_CaptureServiceLogs failed in some of the race unit tests because the log output of PostgreSQL and Redis services were interleaved on multiple lines. InlineServiceLogWriter makes multiple Write() calls to the same sink, so the output in https://gitlab.com/gitlab-org/gitlab-runner/-/jobs/11114656794 had lines such as:

[service:db-postgres] [service:redis-cache] 2025-08-23T04:36:09.130700918Z

Fix this by testing for the prefixes and expected service strings separately to avoid having to match across multiple lines.