feat(db): bound the connection pool with configurable sizing + pre-ping

[amrtgaber]

Follow-up to #47 (the infra hardening it flagged from aoe2-live-standings-api's 2026-06-01 launch incident). Mirrors aoe2 #172.

Problem

app/database.py built the async engine with SQLAlchemy's defaults — pool_size=5, max_overflow=10 = up to 15 connections per instance — and no pool_pre_ping/pool_recycle. On Cloud Run (horizontal scaling) total DB connections = per-instance pool × running instances, and with no instance cap that can saturate Cloud SQL's max_connections (the morning connection-exhaustion outage in the referenced incident). Separately, Cloud SQL silently dropping idle connections surfaces as intermittent request errors without pool_pre_ping.

Change

Make the pool configurable via settings, with conservative defaults:

Setting	Default	Purpose
DB_POOL_SIZE	5	persistent connections per instance
DB_MAX_OVERFLOW	5	burst connections above pool_size (→ 10/instance, down from 15)
DB_POOL_TIMEOUT	30	seconds to wait for a free connection
DB_POOL_RECYCLE	1800	recycle connections older than N seconds
DB_POOL_PRE_PING	true	liveness check before use (handles idle drops)

Applied to Postgres only — SQLite (dev/test) uses a StaticPool that rejects these args, so _pool_kwargs() returns {} for sqlite URLs.

The sizing formula is documented in .env.example:

(DB_POOL_SIZE + DB_MAX_OVERFLOW) × max-instances + migrate-job + headroom ≤ Cloud SQL max_connections

Defaults (10/instance) fit a 200-connection tier at --max-instances=10 (added in the companion deploy PR). Pairs with that instance cap to bound worst-case connections.

Note: this isn't expected to be the bottleneck at current traffic — it's breathing room against a spike, and replaces the unbounded default. Final numbers can be tuned via env once the Cloud SQL tier's max_connections is confirmed.

Test plan

• uv run pytest — 134 passed, 1 skipped
• uv run ruff check . + ruff format --check — clean
• New tests/test_db_pool.py: _pool_kwargs empty for sqlite / populated for postgres; a throwaway asyncpg engine reflects the configured pool.size(); a tripwire test that defaults stay ≤ 10/instance with pre-ping on.