[CI] JNI jobs fail to install archery due to old Python version on images

### Describe the bug, including details regarding any error messages, version, and platform.

Some of the JNI jobs are failing:

Example:

https://github.com/apache/arrow-java/actions/runs/18299702972/job/52105015738

with:

```
Install Archery
Obtaining file:///arrow/dev/archery
Preparing metadata (setup.py): started
Preparing metadata (setup.py): finished with status 'error'
error: subprocess-exited-with-error

× python setup.py egg_info did not run successfully.
│ exit code: 1
╰─> [1 lines of output]
Python < 3.10 is not supported
[end of output]

note: This error originates from a subprocess, and is likely not a problem with pip.

Notice: A new release of pip is available: 24.2 -> 25.2
Notice: To update, run: python -m pip install --upgrade pip
error: metadata-generation-failed

× Encountered error while generating package metadata.
╰─> See above for output.

note: This is an issue with the package mentioned above, not pip.
hint: See above for details.
```

Start with the JNI jobs and their GitHub Actions image or workflow configuration, then inspect the linked action run to identify which environment installs Archery. Verify the Python version used by each failing job and update the relevant CI configuration so Archery installs successfully; done means the JNI jobs pass their Archery installation step.

Written by the indexing model from the issue text.