fix(study/sources): 모바일 카테고리 진입 — drawer + breadcrumb

증상: 모바일에서 좌측 트리 hidden md:block 으로 숨겨져 정렬된 최근
자료 외에는 원하는 카테고리를 찾기 어려움.

Fix:
- 헤더 아래 모바일 전용 (md:hidden) 카테고리 진입 바:
  · "카테고리" 버튼 (FolderTree 아이콘) — 좌측 drawer 띄움
  · breadcrumb: 전체 / 가스기사 / 01_유체역학 / 01_basics
    각 segment 클릭 시 해당 path 로 즉시 이동
  · 가로 스크롤 (overflow-x-auto) — 깊은 path 도 자연스럽게
- aside 좌측 트리 모바일 drawer 화:
  · mobileTreeOpen state. fixed left-0 top-0 bottom-0 w-72 max-w-[85vw]
  · 백드롭 클릭 / X 버튼 / 카테고리 선택 시 자동 닫기
  · 데스크톱(md+)에선 기존 normal layout 유지
- navigateAndClose 헬퍼 — 카테고리 클릭 시 navigate + close 한 번에

frontend/src/routes/study/sources/+page.svelte

@@ -16,7 +16,7 @@
   import { api } from '$lib/api';
   import { addToast } from '$lib/stores/toast';
   import {
-    ChevronRight, ChevronDown, FolderOpen, BookOpen, ArrowLeft,
+    ChevronRight, ChevronDown, FolderOpen, BookOpen, ArrowLeft, FolderTree, X,
   } from 'lucide-svelte';
   import DocumentCard from '$lib/components/DocumentCard.svelte';
   import EmptyState from '$lib/components/ui/EmptyState.svelte';
@@ -124,33 +124,98 @@
   function toggleExpand(path) {
     expanded[path] = !expanded[path];
   }
+
+  // 모바일 트리 drawer
+  let mobileTreeOpen = $state(false);
+  function openTree() { mobileTreeOpen = true; }
+  function closeTree() { mobileTreeOpen = false; }
+  // 카테고리 선택 시 drawer 자동 닫기 (모바일)
+  function navigateAndClose(path) {
+    navigate(path);
+    mobileTreeOpen = false;
+  }
+
+  // 현재 경로 breadcrumb 분해
+  let crumbs = $derived(activePath ? activePath.split('/') : []);
 </script>
 
 <svelte:head><title>자료 학습 — 공부</title></svelte:head>
 
 <div class="h-full flex flex-col">
   <!-- 헤더 -->
-  <div class="flex items-center justify-between gap-2 px-4 py-3 border-b border-default bg-surface shrink-0">
-    <div class="flex items-center gap-2 text-sm">
-      <a href="/study" class="text-dim hover:text-text flex items-center gap-1">
+  <div class="flex items-center justify-between gap-2 px-3 md:px-4 py-2 md:py-3 border-b border-default bg-surface shrink-0">
+    <div class="flex items-center gap-2 text-xs md:text-sm min-w-0">
+      <a href="/study" class="text-dim hover:text-text flex items-center gap-1 shrink-0">
         <ArrowLeft size={14} /> 공부
       </a>
-      <span class="text-faint">/</span>
-      <span class="text-text font-medium flex items-center gap-1.5">
+      <span class="text-faint shrink-0">/</span>
+      <span class="text-text font-medium flex items-center gap-1.5 shrink-0">
         <BookOpen size={14} class="text-accent" /> 자료 학습
       </span>
     </div>
-    <div class="text-xs text-dim">
-      총 {totalCount}건 · <span class="text-text">안 본 {totalUnread}건</span>
+    <div class="text-[10px] md:text-xs text-dim shrink-0">
+      총 {totalCount} · <span class="text-text">안 본 {totalUnread}</span>
     </div>
   </div>
 
-  <div class="flex-1 min-h-0 grid grid-cols-1 md:grid-cols-[260px_1fr] gap-0">
-    <!-- 좌측 트리 -->
-    <aside class="border-r border-default overflow-y-auto p-2 hidden md:block">
+  <!-- 모바일 전용: 카테고리 진입 + breadcrumb -->
+  <div class="md:hidden flex items-center gap-2 px-3 py-2 border-b border-default bg-surface shrink-0 overflow-x-auto">
+    <button
+      type="button"
+      onclick={openTree}
+      style="touch-action: manipulation; user-select: none; -webkit-tap-highlight-color: transparent;"
+      class="flex items-center gap-1 px-3 py-1.5 rounded text-xs bg-accent/10 text-accent border border-accent/30 shrink-0"
+      aria-label="카테고리 선택"
+    >
+      <FolderTree size={14} /> 카테고리
+    </button>
+    {#if crumbs.length > 0}
       <button
         type="button"
         onclick={() => navigate(null)}
+        class="text-xs text-dim hover:text-text shrink-0"
+      >전체</button>
+      {#each crumbs as part, i}
+        <span class="text-faint shrink-0">/</span>
+        <button
+          type="button"
+          onclick={() => navigate(crumbs.slice(0, i + 1).join('/'))}
+          class="text-xs whitespace-nowrap shrink-0
+            {i === crumbs.length - 1 ? 'text-accent font-medium' : 'text-dim hover:text-text'}"
+        >{part}</button>
+      {/each}
+    {:else}
+      <span class="text-xs text-dim shrink-0">전체 자료</span>
+    {/if}
+  </div>
+
+  <div class="flex-1 min-h-0 grid grid-cols-1 md:grid-cols-[260px_1fr] gap-0 relative">
+    <!-- 좌측 트리 (데스크톱 normal, 모바일 drawer overlay) -->
+    {#if mobileTreeOpen}
+      <button
+        type="button"
+        aria-label="카테고리 닫기"
+        onclick={closeTree}
+        class="md:hidden fixed inset-0 z-40 bg-black/40"
+      ></button>
+    {/if}
+    <aside
+      class="border-r border-default overflow-y-auto p-2
+        {mobileTreeOpen ? 'fixed left-0 top-0 bottom-0 w-72 max-w-[85vw] z-50 bg-surface shadow-2xl md:static md:shadow-none md:w-auto md:bg-transparent' : 'hidden md:block'}"
+    >
+      <div class="md:hidden flex items-center justify-between mb-2 px-1">
+        <span class="text-sm font-semibold text-text">카테고리</span>
+        <button
+          type="button"
+          onclick={closeTree}
+          class="p-1 rounded hover:bg-bg text-dim"
+          aria-label="닫기"
+        ><X size={16} /></button>
+      </div>
+      <button
+        type="button"
+        onclick={() => navigateAndClose(null)}
+        style="touch-action: manipulation; user-select: none; -webkit-tap-highlight-color: transparent;"
         class="w-full flex items-center justify-between gap-2 px-2 py-1.5 rounded text-sm transition-colors
           {!activePath ? 'bg-accent/15 text-accent' : 'text-text hover:bg-surface'}"
       >
@@ -185,7 +250,8 @@
 
             <button
               type="button"
-              onclick={() => navigate(n.path)}
+              onclick={() => navigateAndClose(n.path)}
+              style="touch-action: manipulation; user-select: none; -webkit-tap-highlight-color: transparent;"
               class="flex-1 flex items-center justify-between gap-2 px-2 py-1 rounded text-xs transition-colors text-left
                 {isActive ? 'bg-accent/15 text-accent' : isParent ? 'text-text' : 'text-dim hover:bg-surface hover:text-text'}"
               aria-current={isActive ? 'page' : undefined}