perf(gateway): pool backend conns; loadtest evaluate hot path

The loadtest harness never modelled game.evaluate — the debounced per-tile
play preview a real client fires several times per turn, the hottest gameplay
call. Model it (one evaluate per placed tile + reconsideration re-previews +
draft.save, human-paced; --eval / --eval-recon toggle it).

That realistic load surfaced the real bottleneck: the gateway's backend HTTP
client used the default transport (MaxIdleConnsPerHost=2), so every sync call
to the single backend host churned a fresh TCP connection — ~26500 TIME_WAIT
sockets at 500 players (near the ephemeral-port ceiling), burning ~1.75 gateway
cores while the backend sat near-idle. It was the unfixed root of the residual
transport_error the earlier passes chased on the client side.

Widen the keep-alive pool (backendMaxIdleConns=512, ~2x the observed 225-conn
peak). At 500 players the churn collapses to ~0 and peak gateway CPU drops ~7x
(~1.75 -> ~0.26 cores); postgres (~1.65 cores) becomes the busiest service.
This overturns the earlier "gateway is the binding constraint, scale it
horizontally" sizing — that was sizing around this bug, not a real floor.

Consolidate the loadtest trip reports into one loadtest/REPORT.md (drop the
R2/R7 split) and bake the finding into README / PRERELEASE / ARCHITECTURE /
TESTING.

gateway/internal/backendclient/client_internal_test.go

@@ -0,0 +1,31 @@
+package backendclient
+
+import (
+	"net/http"
+	"testing"
+	"time"
+)
+
+// TestBackendTransportPoolsConnections guards the fix for the gateway->backend
+// connection churn. Every synchronous client call proxies to the single backend host,
+// so the REST client must widen the idle-connection pool past the default per-host cap
+// of 2 (http.DefaultMaxIdleConnsPerHost) — otherwise almost every request under load
+// opens a fresh TCP connection that then lingers in TIME_WAIT, burning gateway CPU and
+// exhausting ephemeral ports. Reverting to the default transport (`&http.Client{...}`
+// with no Transport) would silently reintroduce that, so assert the pool is widened.
+func TestBackendTransportPoolsConnections(t *testing.T) {
+	c, err := New("http://backend.invalid", "localhost:9090", time.Second)
+	if err != nil {
+		t.Fatalf("New: %v", err)
+	}
+	defer func() { _ = c.Close() }()
+
+	tr, ok := c.http.Transport.(*http.Transport)
+	if !ok {
+		t.Fatalf("REST transport = %T, want a *http.Transport with a widened idle pool", c.http.Transport)
+	}
+	if tr.MaxIdleConnsPerHost <= http.DefaultMaxIdleConnsPerHost {
+		t.Errorf("MaxIdleConnsPerHost = %d, want > default %d (else per-call connection churn)",
+			tr.MaxIdleConnsPerHost, http.DefaultMaxIdleConnsPerHost)
+	}
+}