SI-1: Migrate health_check context to contract-first architecture

[josecelano]

Subissue of EPIC #1938 — REST API Contract-First Migration

Problem

The health_check endpoint is defined in packages/axum-rest-api-server/src/v1/context/health_check/. Its DTOs (Status, Report) and response logic are defined locally in the Axum server package. Per the contract-first architecture defined in #1930, these should live in rest-api-protocol.

This is the simplest context to migrate — there are zero tracker dependencies.

Scope

• Move Status and Report DTOs from Axum to rest-api-protocol/src/v1/resources/health_check.rs
• Rewire Axum handler to return protocol DTOs
• Remove local DTO definitions from Axum server
• Verify no behavioural change

Checklist

• Protocol DTOs created and exported
• Local DTOs removed from Axum server
• Handler uses protocol DTOs
• Pre-commit checks pass
• Pre-push checks pass

[josecelano]

Implemented via #1946