[FLINK-40124][ci] Do not store cache on every run if no dependency changed

[snuyanzin]

What is the purpose of the change

The problem with current GHA is that it stores cache on every GHA job run even if the cache content was not changed (no dependency changed). The PR is going to fix this.
This can be observed by looking into logs (see into jira issue description for examples)

Brief change log

GHA

Verifying this change

GHA

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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• Yes (please specify the tool below)

[flinkbot]

CI report:

• a0e1657 Azure: SUCCESS

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