Sync eng/common directory with azure-sdk-tools for PR 13563 (#44660)

* Scope changes to codeowners-linter.yml only and use Azure DevOps checkout

Co-authored-by: weshaggard <9010698+weshaggard@users.noreply.github.com>

* Add explanatory comment about shallow clone optimization

Co-authored-by: weshaggard <9010698+weshaggard@users.noreply.github.com>

* Switch from fetchDepth to fetchFilter for branch checkout support

Co-authored-by: weshaggard <9010698+weshaggard@users.noreply.github.com>

---------

Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
Co-authored-by: weshaggard <9010698+weshaggard@users.noreply.github.com>

Author: 3 people

eng/common/pipelines/codeowners-linter.yml

@@ -1,6 +1,5 @@
 # Lint the CODEOWNERS file for a given repository and filter out baseline errors
-# Note: Due to the nature of the verifications, which includes source paths/globs
-# for the repository, this pipeline cannot use sparse-checkout.
+# Uses partial clone (fetchFilter: tree:0) to avoid downloading full git history while allowing branch operations
 trigger: none
 
 pr:
@@ -39,6 +38,10 @@ stages:
       UserOrgUri: "https://azuresdkartifacts.blob.core.windows.net/azure-sdk-write-teams/user-org-visibility-blob"
 
     steps:
+      - checkout: self
+        fetchFilter: tree:0
+        fetchTags: false
+
       - pwsh: |
           dotnet tool install --global --add-source "$(DotNetDevOpsFeed)" --version "$(CodeownersLinterVersion)" "Azure.Sdk.Tools.CodeownersLinter"
         displayName: Install CodeownersLinter