feat(backend): add dependency-aware readiness and recovery diagnostics

[arisu6804]

Problem

A process can report healthy while its database, payment provider, or FX dependency is unavailable.

Objective

Deliver a production-quality improvement to health endpoints and payment/FX dependencies that creates measurable value for correctness, security, reliability, performance, or maintainability.

Implementation scope

• Separate liveness and readiness; add bounded checks and redacted reason codes; ensure recovery does not require restart.

Acceptance criteria

• Liveness remains responsive during outages; readiness accurately changes and recovers; dependency checks cannot hang.

Required validation

• Dependency failure, timeout, recovery, status-code, and redaction tests.
• 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 and explain design tradeoffs, compatibility impact, and test evidence.
• 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.