docs: explain why the matchmaking control plane is Go, fix stale status

Add a Go-vs-C#/Rust/C++ rationale for the matchmaking control plane to
TECH_STACK.md, and point at it from MATCHMAKING.md and README.md.

Also correct CLAUDE.md and README.md, which still described the backend
as unstarted/not built even though server/ has ~13k lines of Go across
matcher, allocator, api, store, security, supervisor and agones.

docs/TECH_STACK.md

@@ -133,6 +133,50 @@ most familiar with. That matches what's independently visible in the repo —
 (`make verify-phase6`), while the systemd unit is native-deployment
 documentation only, with no automated verification of its own.
 
+## Matchmaking control plane: Go, PostgreSQL, Redis, Agones
+
+The one part of the project that is *not* the Godot project. `server/` is a Go
+module (~13k lines of non-test code across `matcher`, `allocator`, `api`,
+`store`, `security`, `supervisor`, `agones`, `migrations`, `observability`)
+implementing the casual/ranked queue design in
+[`MATCHMAKING.md`](MATCHMAKING.md), plus a small PID-1 supervisor that exists
+because Godot/GDScript cannot intercept `SIGTERM` and Agones needs a graceful
+drain signal to land somewhere.
+
+**Why Go, and why "performance" is the wrong reason to give:** the control
+plane is not in the simulation hot path. Physics, snapshots and 60 Hz input
+all live in the Godot dedicated server over ENet/SDR (see the transport
+sections above); Go never touches a game packet. Its actual workload is many
+mostly-idle WebSocket connections, a matcher loop that runs on a sub-second
+tick, and I/O against PostgreSQL, Redis and the Kubernetes API. That is
+I/O- and concurrency-bound, not CPU-bound, so the raw single-thread speed a
+systems language would buy is spent on work this service doesn't do. What
+actually drove the choice:
+
+- **Agones and Kubernetes are Go-native.** Allocation, the GameServer SDK and
+  the k8s client are all first-party Go. Any other language means hand-rolling
+  REST against the Agones allocation service — see `server/agones/`, which uses
+  those clients directly.
+- **Goroutines plus `context` are the right shape for the problem** — many
+  concurrent idle connections, a few periodic loops, and cancel-everything-on-
+  shutdown semantics that the PID-1 supervisor depends on.
+- **The surrounding operational ecosystem is Go** — Prometheus instrumentation
+  (`server/observability/`), structured logging, migrations, and the
+  provider-portable deployment tooling.
+- **Static binaries and slim containers**, which matters for the supervisor and
+  for keeping the allocated game-server image close to the existing one.
+
+**Alternatives, honestly weighed:** Rust or C++ would be the correct answer for
+a custom UDP relay or the simulation server itself, and buy nothing measurable
+for a queue-and-allocate service — while costing significantly in iteration
+speed. C# is the only serious contender (ASP.NET Core is fast, its async model
+is excellent, and Postgres/Redis/WebSocket support is mature); it loses on the
+Agones/Kubernetes side, where the clients are community-maintained rather than
+first-party, and on container weight. TypeScript or Python would prototype
+faster but fit poorly for a service whose failure modes are almost entirely
+races and timeouts. None of those gaps is large enough to justify rewriting the
+Go that already exists.
+
 ## AI opponents: reinforcement learning, trained out-of-process, run in pure GDScript
 
 Two entirely separate pieces, deliberately joined only at a JSON file:
@@ -177,9 +221,11 @@ Python, no .NET, no network." Keeping the shipped game GDScript-only (no
 ## What's deliberately absent
 
 - **No C# or .NET runtime anywhere in the shipped game or server.** The
-  "C# backend" in `README.md`'s early framing was never built. A backend
-  service *is* now planned for matchmaking (see below), but nothing has
-  chosen C# for it — that framing predates every real decision here.
+  "C# backend" an early version of `README.md` described was never built —
+  that wording is long gone from the README itself. A backend
+  service *does* now exist for matchmaking, but it is Go, not C# — that
+  framing predates every real decision here. See "Matchmaking control plane"
+  above for why Go was chosen over C# and over Rust/C++.
 - **No HTTP/WebSocket/gRPC layer for simulation traffic** — the live game uses
   ENet/Steam SDR over UDP via Godot's own `MultiplayerAPI`. The matchmaking
   control plane now has an authenticated Go REST/WebSocket boundary for queue,