[FLINK-40224][ci] Move common scripts out of tools/azure-pipelines

[dalelane]

What is the purpose of the change

Github Actions pipelines use some of the assets from tools/azure-pipelines

This commit moves them into tools/ci to reflect that they are not unique to the AZP builds, and are common across both.

It's a minor refactoring chore, with no functional changes.

Brief change log

Moved some files from tools/azure-pipelines to tools/ci and updated references to match

Verifying this change

Ran Azure pipeline manually to verify
example: https://dev.azure.com/apache-flink/apache-flink/_build/results?buildId=76494&view=results

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

• Yes (please specify the tool below)

[flinkbot]

CI report:

• bbcf78f Azure: SUCCESS

Bot commands

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