96452 Add statsd metrics to ProvidersController

[PhilipDeFraties]

Summary

• Refactored ProviderService#get_provider_service to use with_monitoring

• Ensures StatsD captures total and failed request metrics automatically

• Aligns with the existing pattern in AppointmentsService

• *This work is behind a feature toggle (flipper): NO

Related issue(s)

department-of-veterans-affairs/va.gov-team#96452

Testing done

• existing tests pass

Acceptance criteria

• I fixed|updated|added unit tests and integration tests for each feature (if applicable).
• No error nor warning in the console.
• Events are being sent to the appropriate logging solution
• Documentation has been updated (link to documentation)
• No sensitive information (i.e. PII/credentials/internal URLs/etc.) is captured in logging, hardcoded, or specs
• Feature/bug has a monitor built into Datadog (if applicable)
• If app impacted requires authentication, did you login to a local build and verify all authenticated routes work as expected
• I added a screenshot of the developed feature

Requested Feedback

(OPTIONAL)What should the reviewers know in addition to the above. Is there anything specific you wish the reviewer to assist with. Do you have any concerns with this PR, why?

[randomsync]

This is only going to log a metric on failure, we might want to log it on success as well.

[randomsync]

This is only going to log a metric on failure, we might want to log it on success as well.

[PhilipDeFraties]

closing as per comment in the issue