Use AlertManagement::Payload for processing Prometheus notification

What does this MR do?

This MR builds on !38971 (merged), utilizing new Gitlab::AlertMangement::Payload classes to begin transitioning over AlertManagement code to more uniform APIs.

Specifically, this MR updates the internals of AlertMangement::ProcessPrometheusAlertService to move away from Gitlab::Alerting::Alert and instead use the new tooling added in !38971 (merged).

Screenshots

Does this MR meet the acceptance criteria?

Conformity

• [-] Changelog entry - no user-facing changes. Refactor only.
• [-] Documentation (if required)
• Code review guidelines
• Merge request performance guidelines
• Style guides
• [-] Database guides
• [-] Separation of EE specific content

Availability and Testing

• Review and add/update tests for this feature/bug. Consider all test levels. See the Test Planning Process.
• Tested in all supported browsers
• Informed Infrastructure department of a default or new setting change, if applicable per definition of done