feat(backend): add dependency-aware readiness checks for production health

[arisu6804]

Problem

An always-green health endpoint can route traffic to an instance that cannot reach its database, queue, or chain provider.

Objective

Deliver a production-quality improvement to health endpoints and dependency clients that creates measurable value for correctness, security, reliability, performance, or maintainability.

Implementation scope

• Separate process liveness from dependency readiness.
• Add bounded timeouts and redacted structured status for each required dependency.
• Ensure readiness recovers after transient dependency failure without blocking liveness.

Acceptance criteria

• Liveness remains available during dependency outages.
• Readiness returns a useful non-secret reason and correct status code.
• Dependency checks cannot hang the request or overload downstream services.

Required validation

• Handler tests with each dependency failure, timeout, recovery, and secret-redaction assertions.
• Existing tests and CI remain passing.
• Add regression coverage for the original failure mode.
• Do not weaken, delete, or skip unrelated tests to obtain a green build.

PR quality bar

• Keep the PR focused on this issue and explain design tradeoffs.
• Include test evidence, compatibility impact, and migration or rollout notes where relevant.
• Avoid typo-only, documentation-only, cosmetic-only, or unrelated refactor submissions.

Out of scope

• Broad rewrites not required by the acceptance criteria.
• Changes to unrelated services, contracts, or user flows.