improvement: move bsp responsiveness into status #11345

Job	Run time
windows-latest jdk-17 unit tests 1 / 2	24m 13s
Gradle MacOS integration	17m 2s
windows-latest jdk-17 unit tests 2 / 2	21m 52s
Sbt integration	1h 3m 33s
macOS-latest jdk-17 unit tests 1 / 2	17m 56s
Maven integration	11m 56s
macOS-latest jdk-17 unit tests 2 / 2	19m 58s
Gradle integration	11m 16s
ubuntu-latest jdk-17 unit tests 1 / 2	16m 48s
Scala CLI integration	18m 52s
ubuntu-latest jdk-17 unit tests 2 / 2	15m 7s
Mill integration	18m 49s
ubuntu-latest jdk-8 unit tests 1 / 2	21m 41s
LSP integration tests	34m 40s
ubuntu-latest jdk-8 unit tests 2 / 2	16m 10s
Scala cross tests	54m 21s
Formatting	41s
Scalafix and docs	9m 33s
Sbt-metals/scripted jdk8	1m 56s
Scala javapc tests	2m 18s
Scala3 latest NIGHTLY cross test	4m 21s
MiMa	1m 1s
	6h 44m 4s

Provide feedback