[hotfix][build] Use sparse-checkout paths for Flink template in GHA.

[snuyanzin]

What is the purpose of the change

No need to run full repo checkout each time since (in e2e and test tasks)

Brief change log

(for example:)

• The TaskInfo is stored in the blob store on job creation time as a persistent artifact
• Deployments RPC transmits only the blob storage reference
• TaskManagers retrieve the TaskInfo from the blob cache

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? (yes / no)
• If yes, how is the feature documented? (not applicable / docs / JavaDocs / not documented)

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Was generative AI tooling used to co-author this PR?

• Yes (please specify the tool below)

[flinkbot]

CI report:

• 82b7e7a Azure: SUCCESS

Bot commands

The @flinkbot bot supports the following commands:

• @flinkbot run azure re-run the last Azure build

[raminqaf]

LGTM