test(health): add router-level coverage for /healthz/ready database-unavailable path

[NotThatKindOfDrLiz]

PR #93 adds function-level health probe coverage, but the router-level tests do not exercise the /healthz/ready database-unavailable path end to end.

Requested follow-up:

• extend the router smoke tests to hit /healthz/ready
• use sqlx::PgPool::connect_lazy against an unreachable URL so the database-unavailable path can be exercised through the router
• assert the end-to-end 503 Database unavailable behavior

Context:

• This was suggested as a non-blocking follow-up in review on PR Improve keycast health probes #93.
• The current pure-function tests already catch most regressions; this would strengthen end-to-end confidence.

This is non-blocking for PR #93 but would improve coverage of the new readiness behavior.

[sergey3bv]

Hey, @NotThatKindOfDrLiz, I opened a PR to solve the issue, could you please take a look?

cc @rabble