Fix test result publishing

[lbussell]

See #1246

• Testing this fix in PR validation since it affects public builds
• Rearrange docker copy and test results check commands

[dotnet-issue-labeler]

I couldn't figure out the best area label to add to this PR. If you have write-permissions please help me learn by adding exactly one area label.

[lbussell]

/azp run

[azure-pipelines]

Azure Pipelines failed to run 1 pipeline(s).

[lbussell]

The correct solution to the issue of having no test results to publish is #1250.

[lbussell]

This change should go in as-is and #1250 should be addressed separately so that test results are available again as soon as possible.