perf(db): raise Prisma pg.Pool max to 20 for power-user fan-out headroom

The v1.4.39 empirical cold-mount trace
(`.planning/round-v1439-empirical-trace.md` §B2) flagged the library
default of 10 concurrent connections as the hard ceiling that thick
/api/analytics was monopolising. With the parallel W-POOL p-limit(4)
cap on the analytics fan-out, a 20-slot pool leaves ≥16 free slots for
every other dashboard query regardless of how many measurement types
analytics is mid-walk over. Postgres' stock `max_connections` of 100
gives ample headroom for ≤5 concurrent power-users at this ceiling.
Env-overridable via `DATABASE_POOL_MAX` so operators with a smaller
server-side `max_connections` can dial down without a code change.

src/lib/db.ts

@@ -5,9 +5,40 @@ const globalForPrisma = globalThis as unknown as {
   prisma: PrismaClient | undefined;
 };
 
+/**
+ * v1.4.40 W-POOL — Prisma `pg.Pool` ceiling raised from the library
+ * default of 10 → 20.
+ *
+ * The v1.4.39 empirical cold-mount trace
+ * (`.planning/round-v1439-empirical-trace.md` § B2) showed thick
+ * `/api/analytics` holding ≥ 8 of the 10 default pool slots for
+ * 6.5 s on Marc's 347k-row tenant, starving every other Wave-B and
+ * Wave-C useQuery fan-out for the duration. Coolify's Postgres
+ * container runs the stock `max_connections` 100 ceiling, so a
+ * 20-slot Node-side pool sits well under the server's hard cap with
+ * plenty of headroom for concurrent power-users (≤ 5 simultaneous
+ * tenants × 20 = 100). Complements the W-POOL `p-limit(4)` cap on
+ * the analytics fan-out itself — the bounded concurrency keeps any
+ * single analytics call to ≤ 4 slots, so the remaining 16 stay
+ * available for every other dashboard query.
+ *
+ * Env-overridable via `DATABASE_POOL_MAX` so an operator running
+ * with a smaller Postgres `max_connections` can dial down without a
+ * code change.
+ */
+export function getPoolMax(): number {
+  const raw = process.env.DATABASE_POOL_MAX;
+  if (raw) {
+    const parsed = Number.parseInt(raw, 10);
+    if (Number.isFinite(parsed) && parsed > 0) return parsed;
+  }
+  return 20;
+}
+
 function createPrismaClient() {
   const adapter = new PrismaPg({
     connectionString: process.env.DATABASE_URL!,
+    max: getPoolMax(),
   });
   return new PrismaClient({ adapter });
 }