Ensure Rush bootstrap precedes npmrc clearing in Azure publish pipelines

[Copilot]

This updates the Azure publish flow so user-level npm registry override does not block Rush bootstrap. Rush is now installed first, then ~/.npmrc is cleared before publish/pack steps that must target the public registry.

• Publish-flow ordering

  • Added an explicit Rush bootstrap step at the start of both publish templates:
    • common/config/azure-pipelines/templates/publish.yaml
    • common/config/azure-pipelines/templates/pack.yaml
  • Bootstrap uses install-run-rush with --help to ensure Rush is available before registry cleanup.

• Registry cleanup timing

  • Kept the existing rm -f "$HOME/.npmrc" behavior, but moved it to run after Rush bootstrap and before rush publish --publish flows.

• Resulting execution pattern

  • Install Rush → Clear user npmrc for publish → Rush publish/pack

steps:
  - template: /common/config/azure-pipelines/templates/install-run-rush.yaml@self
    parameters:
      Arguments: '--help'
      DisplayName: 'Install Rush'

  - bash: 'rm -f "$HOME/.npmrc"'
    displayName: 'Clear user npmrc for publish'