chore: add debug logs to server liveness monitor #11371

Job	Run time
Gradle MacOS integration	16m 22s
windows-latest jdk-17 unit tests 1 / 2	34m 34s
Sbt integration	55m 52s
windows-latest jdk-17 unit tests 2 / 2	22m 1s
Maven integration	11m 15s
macOS-latest jdk-17 unit tests 1 / 2	31m 55s
Gradle integration	12m 25s
macOS-latest jdk-17 unit tests 2 / 2	20m 16s
Scala CLI integration	20m 27s
ubuntu-latest jdk-17 unit tests 1 / 2	17m 57s
Mill integration	15m 20s
ubuntu-latest jdk-17 unit tests 2 / 2	14m 30s
LSP integration tests	37m 44s
ubuntu-latest jdk-8 unit tests 1 / 2	25m 29s
Scala cross tests	1h 1m 42s
ubuntu-latest jdk-8 unit tests 2 / 2	17m 15s
Formatting	39s
Scalafix and docs	9m 32s
Sbt-metals/scripted jdk8	2m 39s
Scala javapc tests	2m 47s
Scala3 latest NIGHTLY cross test	4m 16s
MiMa	1m 9s
	7h 16m 6s

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