Migrate Azure.Mcp.Tools.ConfidentialLedger.LiveTests LiveTests to Recorded Tests

Migrate tests within tools/Azure.Mcp.Tools.ConfidentialLedger/tests/Azure.Mcp.Tools.ConfidentialLedger.LiveTests/Azure.Mcp.Tools.ConfidentialLedger.LiveTests.csproj to recordings. Utilize copilot to assist with the migration process for Azure.Mcp.Tools.ConfidentialLedger.LiveTests.
- For additional guidance check [the recorded tests document](https://github.com/microsoft/mcp/blob/main/docs/recorded-tests.md)

This task will be considered complete when the livetests can be invoked without the presence of a .testsettings.json file.

Submit a PR with your change and verify that the recorded tests are running in the [recorded test step](https://dev.azure.com/azure-sdk/internal/_build/results?buildId=5627747&view=logs&jobId=1e679852-4871-5dae-dd38-eb073eb853d4&j=1e679852-4871-5dae-dd38-eb073eb853d4&t=2f22000c-4a69-5b6e-fbac-d06c3b6f57da)