fix(picloud): F-P-003 PICLOUD_DB_MAX_CONNECTIONS env knob, default 32 (matches gate)

init_db hard-coded max_connections(10). The execution gate
(ExecutionGate, PICLOUD_MAX_CONCURRENT_EXECUTIONS default 32) lets 32
script executions run concurrently, each doing multiple sequential
DB calls — plus the dispatcher tick every 100ms, the cron tick, three
GC sweeps, and the auth middleware running per request all draw from
the same pool. With max=10 vs gate=32, pool starvation surfaces as
acquire_timeout errors and tail-latency spikes under load.

- DEFAULT_DB_MAX_CONNECTIONS = 32 (matches gate default).
- Env knob: PICLOUD_DB_MAX_CONNECTIONS overrides; invalid/zero → default.
- Documented in CLAUDE.md runtime config table.

AUDIT.md anchor: F-P-003.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

crates/picloud/src/lib.rs

@@ -588,11 +588,25 @@ pub async fn build_app(
         .layer(TraceLayer::new_for_http()))
 }
 
+/// Default Postgres pool size. Scaled to match the execution gate
+/// default (32 concurrent script executions) so a hot pool doesn't
+/// starve the data plane. Override with `PICLOUD_DB_MAX_CONNECTIONS`.
+/// Sizing relationship: each script run does multiple sequential DB
+/// calls (script resolve, SDK calls, log sink, outbox emit) plus the
+/// dispatcher tick / cron tick / GC sweeps / auth middleware all draw
+/// from the same pool, so this is a floor not a ceiling.
+pub const DEFAULT_DB_MAX_CONNECTIONS: u32 = 32;
+
 /// Open a Postgres pool with the binary's standard timeout settings.
 /// Exposed so tests reach for the same configuration when needed.
 pub async fn init_db(url: &str) -> anyhow::Result<PgPool> {
+    let max_connections = std::env::var("PICLOUD_DB_MAX_CONNECTIONS")
+        .ok()
+        .and_then(|v| v.trim().parse::<u32>().ok())
+        .filter(|n| *n > 0)
+        .unwrap_or(DEFAULT_DB_MAX_CONNECTIONS);
     let pool = PgPoolOptions::new()
-        .max_connections(10)
+        .max_connections(max_connections)
         .acquire_timeout(Duration::from_secs(5))
         .connect(url)
         .await?;