[Tables] Migrate to new test proxy

[YalinLi0312]

For issue: #20114

[scbedd]

@YalinLi0312 tomorrow I will add the necessary changes to spin up the test-proxy!

[check-enforcer]

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[azure-sdk]

API changes have been detected in azure-data-tables. You can review API changes here

[mccoyp]

Running a new pipeline that will (or should) have test proxy logs here: https://dev.azure.com/azure-sdk/public/_build/results?buildId=1221035&view=results

[mccoyp]

/azp run python - tables - tests

[azure-pipelines]

Azure Pipelines successfully started running 1 pipeline(s).

[mccoyp]

/azp run python - tables - tests

[azure-pipelines]

Azure Pipelines successfully started running 1 pipeline(s).

[mccoyp]

/azp run python - tables - tests

[azure-pipelines]

Azure Pipelines successfully started running 1 pipeline(s).

[mccoyp]

/azp run python - tables - tests

[azure-pipelines]

Azure Pipelines successfully started running 1 pipeline(s).

[mccoyp]

/azp run python - tables - tests

[azure-pipelines]

Azure Pipelines successfully started running 1 pipeline(s).

[mccoyp]

/azp run python - tables - tests

[azure-pipelines]

Azure Pipelines successfully started running 1 pipeline(s).

[mccoyp]

/azp run python - tables - tests

[azure-pipelines]

Azure Pipelines successfully started running 1 pipeline(s).

[mccoyp]

/azp run python - tables - tests

[azure-pipelines]

Azure Pipelines successfully started running 1 pipeline(s).

[mccoyp]

/azp run python - tables - tests

[azure-pipelines]

Azure Pipelines successfully started running 1 pipeline(s).

[mccoyp]

/azp run python - tables - tests

[azure-pipelines]

Azure Pipelines successfully started running 1 pipeline(s).

[mccoyp]

/azp run python - tables - tests

[azure-pipelines]

Azure Pipelines successfully started running 1 pipeline(s).