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.

docs/ARCHITECTURE.md

@@ -128,7 +128,11 @@ dropped). Horizontal scaling is explicit future work.
   and GCG are unaffected** (they stay decoded concrete characters, §9.1).
 - **gateway ↔ backend (sync)**: plain HTTP REST/JSON. The gateway injects
   `X-User-ID` for authenticated requests; `backend` never re-derives identity
-  from the body.
+  from the body. Because every sync call targets the one backend host, the
+  gateway's REST client widens its keep-alive pool well past the stdlib default
+  of 2 idle connections per host; otherwise the per-request connection churn
+  exhausts ephemeral ports and burns gateway CPU under load (see
+  [`../loadtest/REPORT.md`](../loadtest/REPORT.md)).
 - **backend → gateway (live)**: a single gRPC server-stream carries live events
   (your-turn, opponent-moved, chat, nudge). The gateway bridges them to the
   client's in-app stream while the app is open. Out-of-app delivery uses

docs/TESTING.md

@@ -133,9 +133,9 @@ tests or touching CI.
   engine tests do). It is **not** part of the per-PR suite's behavioural assertions: it
   runs ad hoc as a one-shot container against the contour, producing a trip report (bugs
   + a per-container resource profile) read off the **otelcol `docker_stats` +
-  postgres_exporter** Grafana dashboard on the contour. Two passes are recorded — the
-  early [`REPORT-R2.md`](../loadtest/REPORT-R2.md) and the final, tuned
-  [`REPORT-R7.md`](../loadtest/REPORT-R7.md). See [`../loadtest/README.md`](../loadtest/README.md).
+  postgres_exporter** Grafana dashboard on the contour. The findings — including the
+  `game.evaluate` hot-path model and the gateway→backend connection-pool fix — are written
+  up in [`REPORT.md`](../loadtest/REPORT.md). See [`../loadtest/README.md`](../loadtest/README.md).
 - **User feedback** — `internal/feedback` unit tests cover the attachment allow-list /
   content-type and the channel normaliser; the UI covers `detectChannel`, the attachment gate and
   the feedback wire round-trip (`channel` / `feedback` / `codec` tests) plus a Playwright e2e