feat(hunt): track walking distance via GPS, show live locations on map

Add foreground-only GPS distance tracking for hunts

shared/types/map.ts

@@ -0,0 +1,58 @@
+/**
+ * Shared DTO shapes for the organizer live map. Both endpoints return plain
+ * JSON (no SuperJSON) with `Date` fields serialized as ISO strings and Prisma
+ * `Decimal` coordinates coerced to numbers.
+ */
+
+export type MapUser = {
+  id: number;
+  name: string;
+  email: string;
+};
+
+export type MapTeam = {
+  id: number;
+  name: string;
+  owner: MapUser;
+  members: MapUser[];
+};
+
+export type MapPosition = {
+  userId: number;
+  lat: number;
+  lon: number;
+  accuracy: number | null;
+  recordedAt: string;
+};
+
+export type MapAnswer = {
+  id: number;
+  lat: number;
+  lon: number;
+  createdAt: string;
+  memberId: number;
+  teamId: number;
+  pictureUrl: string | null;
+  quest: {
+    id: number;
+    title_de: string;
+    title_en: string;
+  };
+};
+
+export type HuntMapData = {
+  teams: MapTeam[];
+  positions: MapPosition[];
+  answers: MapAnswer[];
+};
+
+export type TrailPoint = {
+  lat: number;
+  lon: number;
+  accuracy: number | null;
+  recordedAt: string;
+};
+
+export type UserTrail = {
+  points: TrailPoint[];
+};