Enable profiling for database benchmarks

[tuliren]

• Depends on Run database benchmarks in cloud #8640.
• Enable Sentry Experiment with Sentry performance monitoring for BigQuery destination #9328
• Enable Datadog
• Make a decision on which one we want to support
• Next steps (if needed) for what platform changes are required to make it work (e.g: injecting env variables or something, do we want it in both OSS and Cloud, etc..)
• Relevant to [EPIC] Integrate Sentry #7956

[tuliren]

This issue depends on #8640, which depends on #8729. We probably cannot finish it this sprint.

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Update: the above blockers have been resolved.

[evantahler]

Closing in favor of #15152