Sync eng/common directory with azure-sdk-tools for PR 6982 (Azure#36792)

* update proxy version

* remove proxy checkout in favor of allowing tooling checkout

---------

Co-authored-by: Scott Beddall (from Dev Box) <[email protected]>

Author: azure-sdk

eng/common/testproxy/target_version.txt

@@ -1 +1 @@
-1.0.0-dev.20230818.1
+1.0.0-dev.20230912.4

eng/pipelines/templates/jobs/ci.tests.yml

@@ -79,10 +79,6 @@ jobs:
         parameters:
           runProxy: true
 
-      - template: /eng/pipelines/templates/steps/restore-test-proxy-recordings.yml
-        parameters:
-          Paths: $(SparseCheckoutDirectories)
-
       - pwsh: |
           $files = Get-ChildItem -Path $(Build.SourcesDirectory) -Filter test-proxy.log
           foreach($file in $files){

eng/pipelines/templates/jobs/ci.versions.tests.yml

@@ -69,10 +69,6 @@ jobs:
         parameters:
           runProxy: true
 
-      - template: /eng/pipelines/templates/steps/restore-test-proxy-recordings.yml
-        parameters:
-          Paths: $(SparseCheckoutDirectories)
-
       - pwsh: |
           $files = Get-ChildItem -Path $(Build.SourcesDirectory) -Filter test-proxy.log
           foreach($file in $files){