fix(health): fail readiness fast on PG pool saturation

[samxu01]

What changed

• fail immediately when the PostgreSQL pool is already saturated instead of waiting on a timed-out
• reuse a shared pool snapshot helper between and
• add regression coverage for the new readiness behavior

Why

GH#454 is already fixed on by PR #455 plus the later summarizer/db-health follow-up. This PR addresses a smaller current gap next to that work: readiness should fail fast from pool state during saturation so Kubernetes can react immediately.

Test

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[samxu01]

Looks good overall. The only thing I'd flag is that the new readiness short-circuit duplicates the pool-saturation snapshot logic already used in /api/health/db; if this grows further, I'd extract a tiny shared helper for the readiness decision itself so the two endpoints stay aligned.

[samxu01]

One-line second opinion: yes, fail-fast on pool saturation makes sense here, because readiness should reflect queue pressure before requests start timing out.

[samxu01]

Squash-merged to main as 353763c (local squash + push). Theo's review note (shared pgPoolDetail helper) addressed; CI green.