refactor(ai-gateway): compose application with Effect

[robinbraemer]

Progresses #105
Progresses #102
Progresses #107

Outcome

Composes the Effect-native AI Gateway application over the new forwarding, provider HTTP, quota, account-vault, routing-state, and settlement services. It owns readiness, protected status, bounded quota caching, OAuth/API-key route selection, lease renewal/release, 401 reauthentication bookkeeping, and request forwarding without Promise orchestration.

Behavior

• Health remains public; readiness reflects credential/capacity state.
• Status requires the operator credential and returns no provider credential or payload.
• Healthy quota is probed once and reused only within the bounded cache window.
• OAuth routes inject the selected access token/account ID only.
• API-key fallback is impossible unless both explicitly enabled and configured.
• Terminal usage is settled exactly through the authenticated reporter.

Verification

• AI Gateway legacy characterization: 64 passed
• Effect suite: 219 passed across 41 files
• Effect policy: 395 TypeScript paths, zero violations
• build, root typecheck, and diff check passed

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Status	Name	Latest Commit	Updated (UTC)
❌ Deployment failed View logs	agentos-site	0fe649a	Aug 01 2026, 07:41 PM

[robinbraemer]

Required check passed. Local evidence: 64 AI Gateway legacy characterization tests, 219 Effect tests across 41 files, Effect policy over 395 TypeScript paths with zero violations, plus build, root typecheck, and diff check. The external Workers Builds: agentos-site integration failed and its dependent website preview remains pending, matching prior PRs; this PR does not change the website.