fix(server): name the player on every played word, and bound the process

PlayedWord.player_id was declared and read by the client but never set by
the server, so a room of three or four never showed who played each word.
The chain byline now comes from the room, with a producer-side test.

The process also gains the ceilings it was missing: a cap on live rooms and
on open sockets, a per-connection frame-rate limit so a payload-less frame
is no longer free, and an opt-in trusted-proxy list so the join limiter can
tell players apart behind the documented reverse proxy instead of putting
them in one bucket. The typed word is sanitized before the engine stores it,
since every seat is shown it; a room exiting on its idle clock releases the
sessions still bound to it; the dictionary builder escapes its SQLite path
like the store does and renames over the old database instead of deleting
it first.

server/cmd/noitu-server/main.go

@@ -9,6 +9,7 @@ import (
 	"net/http"
 	"os"
 	"os/signal"
+	"strconv"
 	"strings"
 	"syscall"
 	"time"
@@ -36,6 +37,9 @@ type config struct {
 	grace          time.Duration
 	allowedOrigins []string
 	webDir         string
+	trustedProxies []string
+	maxRooms       int
+	maxConnections int
 }
 
 func main() {
@@ -74,6 +78,9 @@ func run() error {
 		GraceFor:       cfg.grace,
 		AllowedOrigins: cfg.allowedOrigins,
 		WebDir:         cfg.webDir,
+		TrustedProxies: cfg.trustedProxies,
+		MaxRooms:       cfg.maxRooms,
+		MaxConnections: cfg.maxConnections,
 	})
 
 	srv := &http.Server{
@@ -114,9 +121,27 @@ func loadConfig() config {
 		grace:          envDuration("NOITU_GRACE", defaultGrace),
 		allowedOrigins: envList("NOITU_ALLOWED_ORIGINS"),
 		webDir:         env("NOITU_WEB_DIR", ""),
+		trustedProxies: envList("NOITU_TRUSTED_PROXIES"),
+		maxRooms:       envInt("NOITU_MAX_ROOMS", 0),
+		maxConnections: envInt("NOITU_MAX_CONNECTIONS", 0),
 	}
 }
 
+// envInt falls back loudly, like envDuration. Zero means "use the built-in
+// default", so it is what an unset or invalid value becomes.
+func envInt(key string, fallback int) int {
+	raw := strings.TrimSpace(os.Getenv(key))
+	if raw == "" {
+		return fallback
+	}
+	n, err := strconv.Atoi(raw)
+	if err != nil || n < 0 {
+		slog.Warn("ignoring invalid integer", "key", key, "value", raw, "using", fallback)
+		return fallback
+	}
+	return n
+}
+
 func env(key, fallback string) string {
 	if v := strings.TrimSpace(os.Getenv(key)); v != "" {
 		return v