[CI] Stop running Packaging Linux jobs on Push to main #55261

Describe the enhancement requested

On:

• GH-51643: [CI] Run extra jobs on pushes to main again #51666

We re-added the ability for extra jobs to run when pushed to main because of JNI dockerfile images not being generated:

• [CI] Publish updated cpp-jni images with Python 3.11 #51643

The Linux Packaging jobs take a lot of resources and there are no Dockerfile images to be generated. We could remove them from running when pushing to main as they are run on nightlies and on PRs when required via the extra labels.

Component(s)

Continuous Integration