[FLINK-33906][ci] tools/azure-pipelines/debug_files_utils.sh should support GHA output as well

[XComp]

Based on the following PR(s):

• https://github.com/apache/flink/pull/23961
• https://github.com/apache/flink/pull/23962
• https://github.com/apache/flink/pull/23965
• https://github.com/apache/flink/pull/24061
• === THIS PR ===
• https://github.com/apache/flink/pull/23970
• https://github.com/apache/flink/pull/23971
• https://github.com/apache/flink/pull/23972

What is the purpose of the change

See FLINK-33906 for further context.

Brief change log

• Adds support for GHA environment variables

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

[flinkbot]

CI report:

• d9c3ecb9709d1e7ab149156390554aae6154c240 Azure: SUCCESS

Bot commands

The @flinkbot bot supports the following commands:

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

[XComp]

I created FLINK-34038 to cover the test failure. It's unrelated to this change.

[XComp]

I rebased the change onto master after the preceeding PR of FLINK-34047 was merged to master