fix(frontend): use relative URLs to support reverse proxy subpath (/sync/)

app/static/app.js

@@ -19,7 +19,7 @@ document.addEventListener("DOMContentLoaded", () => {
     if (!url) return;
 
     try {
-      const res = await fetch("/api/download", {
+      const res = await fetch("api/download", {
         method: "POST",
         headers: { "Content-Type": "application/json" },
         body: JSON.stringify({ url })
@@ -40,7 +40,7 @@ document.addEventListener("DOMContentLoaded", () => {
   syncLikesBtn.addEventListener("click", async () => {
     if (!confirm("Запустить синхронизацию плейлиста «Мне нравится» из Яндекс Музыки?")) return;
     try {
-      const res = await fetch("/api/sync/yandex-likes", { method: "POST" });
+      const res = await fetch("api/sync/yandex-likes", { method: "POST" });
       const data = await res.json();
       if (data.task_id) {
         fetchTasks();
@@ -52,7 +52,7 @@ document.addEventListener("DOMContentLoaded", () => {
 
   async function fetchTasks() {
     try {
-      const res = await fetch("/api/tasks");
+      const res = await fetch("api/tasks");
       const tasks = await res.json();
       renderTasks(tasks);
     } catch (err) {
@@ -87,7 +87,7 @@ document.addEventListener("DOMContentLoaded", () => {
 
   async function fetchHistory() {
     try {
-      const res = await fetch("/api/history");
+      const res = await fetch("api/history");
       const data = await res.json();
       if (tracksCount) tracksCount.textContent = `Загружено: ${data.total || 0}`;
       renderHistory(data.tracks || []);