[CI] Stabilize Connection stability test: Only run test on net 10, only print per node status in debug runs

[romanett]

Proposed changes

Connection Stability Test failed on net 472 due to missing mono dependency.
Stabilize Connection stability test: Only run test on net 10, only print per node status in debug runs

Related Issues

• Fixes Long running tests need to pass #3423

Types of changes

• Bugfix (non-breaking change which fixes an issue)
• Enhancement (non-breaking change which adds functionality)
• Test enhancement (non-breaking change to increase test coverage)
• Breaking change (fix or feature that would cause existing functionality to not work as expected, requires version increase of Nuget packages)
• Documentation Update (if none of the other choices apply)

Checklist

• I have read the CONTRIBUTING doc.
• I have signed the CLA.
• I ran tests locally with my changes, all passed.
• I fixed all failing tests in the CI pipelines.
• I fixed all introduced issues with CodeQL and LGTM.
• I have added tests that prove my fix is effective or that my feature works and increased code coverage.
• I have added necessary documentation (if appropriate).
• Any dependent changes have been merged and published in downstream modules.