[FLINK-34897][test] Enables JobMasterServiceLeadershipRunnerTest#testJobMasterServiceLeadershipRunnerCloseWhenElectionServiceGrantLeaderShip again.

[XComp]

PR Chain

• *** THIS PR ***
• [FLINK-34933][test] Fixes JobMasterServiceLeadershipRunnerTest#testResultFutureCompletionOfOutdatedLeaderIsIgnored #24562
• [FLINK-34939][test] Hardens TestingLeaderElection #24568
• [FLINK-34672][runtime] Fixes deadlock risk in DefaultLeaderElectionService #24561

What is the purpose of the change

It seems like I disabled the test accidentally with FLINK-31783. This PR re-enables the test (and fixes it).

Brief change log

• Enables test again
• Makes the test wait for the leadership being confirmed by polling the leader information in the HA backend rather than relying on hasLeadership

Verifying this change

This change is a trivial rework / code cleanup without any test coverage.

Does this pull request potentially affect one of the following parts:

• Dependencies (does it add or upgrade a dependency): no
• The public API, i.e., is any changed class annotated with @Public(Evolving): no
• The serializers: no
• The runtime per-record code paths (performance sensitive): no
• Anything that affects deployment or recovery: JobManager (and its components), Checkpointing, Kubernetes/Yarn, ZooKeeper: no
• The S3 file system connector: no

Documentation

• Does this pull request introduce a new feature? no
• If yes, how is the feature documented? not applicable

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CI report:

• 40cfa0b Azure: SUCCESS

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