feat(gateway): /g/:slug proxy data plane with key auth and rate limits (#66)

The admin surface under /admin/gateway managed api_services and api_keys,
but no public route ever consumed them. Mounts /g/:slug and /g/:slug/* on
the root router (outside /api/v1 so route_prefix stays clean) and runs the
full pipeline: slug lookup -> X-API-Key/Bearer extraction -> prefix-indexed
bcrypt key auth -> allowed_service_ids scope -> per-minute buckets (key and
service caps) -> monthly usage_counters quotas -> gateway.ProxyRequest with
per-service timeout and upstream auth headers -> usage/metrics/incident
recording.

Live-verified: proxied GET/POST, 401/404/429 boundaries, counter upserts,
UPSTREAM_5XX incidents. Unit tests cover URL building, the rpm bucket, key
extraction, and the service allowlist.

Generated with [Devin](https://devin.ai)

Co-authored-by: Devin <158243242+devin-ai-integration[bot]@users.noreply.github.com>

app/backend/internal/api/gateway_proxy_test.go

@@ -0,0 +1,81 @@
+package api
+
+import (
+	"net/http/httptest"
+	"testing"
+	"time"
+
+	"github.com/gin-gonic/gin"
+)
+
+func TestGatewayRateAllow(t *testing.T) {
+	now := time.Date(2026, 10, 15, 12, 0, 30, 0, time.UTC)
+
+	for i := 0; i < 3; i++ {
+		if !gatewayRateAllow("test:a", 3, now) {
+			t.Fatalf("call %d within limit rejected", i+1)
+		}
+	}
+	if gatewayRateAllow("test:a", 3, now) {
+		t.Fatal("call beyond limit allowed")
+	}
+	if !gatewayRateAllow("test:a", 3, now.Add(time.Minute)) {
+		t.Fatal("new minute window still rejected")
+	}
+	if !gatewayRateAllow("test:unlimited", 0, now) {
+		t.Fatal("non-positive limit should disable the check")
+	}
+}
+
+func TestExtractGatewayKey(t *testing.T) {
+	mkctx := func(headers map[string]string) *gin.Context {
+		c, _ := gin.CreateTestContext(httptest.NewRecorder())
+		c.Request = httptest.NewRequest("GET", "/g/x", nil)
+		for k, v := range headers {
+			c.Request.Header.Set(k, v)
+		}
+		return c
+	}
+
+	if got := extractGatewayKey(mkctx(map[string]string{"X-API-Key": "ap_abc"})); got != "ap_abc" {
+		t.Fatalf("X-API-Key not extracted: %q", got)
+	}
+	if got := extractGatewayKey(mkctx(map[string]string{"Authorization": "Bearer ap_def"})); got != "ap_def" {
+		t.Fatalf("Bearer not extracted: %q", got)
+	}
+	// X-API-Key wins when both are present.
+	if got := extractGatewayKey(mkctx(map[string]string{
+		"X-API-Key":     "ap_first",
+		"Authorization": "Bearer ap_second",
+	})); got != "ap_first" {
+		t.Fatalf("X-API-Key should take precedence: %q", got)
+	}
+	if got := extractGatewayKey(mkctx(map[string]string{})); got != "" {
+		t.Fatalf("expected empty key, got %q", got)
+	}
+}
+
+func TestKeyAllowsService(t *testing.T) {
+	svcID := "11111111-2222-3333-4444-555555555555"
+	other := "aaaaaaaa-bbbb-cccc-dddd-eeeeeeeeeeee"
+
+	cases := []struct {
+		name    string
+		allowed string
+		want    bool
+	}{
+		{"empty list permits all", "[]", true},
+		{"blank permits all", "", true},
+		{"invalid json permits all", "not-json", true},
+		{"listed service allowed", `["` + svcID + `"]`, true},
+		{"unlisted service denied", `["` + other + `"]`, false},
+	}
+	for _, tc := range cases {
+		t.Run(tc.name, func(t *testing.T) {
+			k := &gatewayKey{AllowedServiceIDs: tc.allowed}
+			if got := keyAllowsService(k, svcID); got != tc.want {
+				t.Fatalf("keyAllowsService(%q) = %v, want %v", tc.allowed, got, tc.want)
+			}
+		})
+	}
+}