[Monitor Ingestion] Refactor Monitor Ingestion tests to work with latest TestProxy

[g2vinay]

To address the timeout issues with azure-monitor-ingestion tests when using the latest Test Proxy, the tests are marked live only as part of this PR: #39935.

The central sanitization process on the recordings may be causing the timeouts, so re-record and opt out of sanitizers that are causing any issues with the tests.

Need to figure out what central sanitizers should be disabled or refactoring the tests to make it compatible with the sanitization process, ensuring they can run without the need for live-only conditions. This will likely involve adjusting the test setup, and the data validation steps within the tests.

Reach out to @samvaity and @scbedd for any assistance with this.