모바일 필터 바텀시트 UI 적용

- FilterSheet 컴포넌트 신규: 바텀시트로 올라오는 필터 선택 UI
- 장르/가격/지역 필터 모두 네이티브 select 대신 바텀시트 사용
- 카테고리별 그룹핑 + sticky 헤더 + 선택 체크 표시
- slide-up 애니메이션 추가

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

frontend/src/components/FilterSheet.tsx

@@ -0,0 +1,112 @@
+"use client";
+
+import { useEffect, useRef } from "react";
+import Icon from "@/components/Icon";
+
+export interface FilterOption {
+  label: string;
+  value: string;
+  group?: string;
+}
+
+interface FilterSheetProps {
+  open: boolean;
+  onClose: () => void;
+  title: string;
+  options: FilterOption[];
+  value: string;
+  onChange: (value: string) => void;
+}
+
+export default function FilterSheet({ open, onClose, title, options, value, onChange }: FilterSheetProps) {
+  const sheetRef = useRef<HTMLDivElement>(null);
+
+  useEffect(() => {
+    if (!open) return;
+    document.body.style.overflow = "hidden";
+    return () => { document.body.style.overflow = ""; };
+  }, [open]);
+
+  // Group options by group field
+  const grouped = options.reduce<Record<string, FilterOption[]>>((acc, opt) => {
+    const key = opt.group || "";
+    if (!acc[key]) acc[key] = [];
+    acc[key].push(opt);
+    return acc;
+  }, {});
+  const groups = Object.keys(grouped);
+
+  const handleSelect = (v: string) => {
+    onChange(v);
+    onClose();
+  };
+
+  if (!open) return null;
+
+  return (
+    <>
+      {/* Backdrop */}
+      <div
+        className="fixed inset-0 z-[60] bg-black/30 md:hidden"
+        onClick={onClose}
+      />
+
+      {/* Sheet */}
+      <div
+        ref={sheetRef}
+        className="fixed bottom-0 left-0 right-0 z-[61] md:hidden bg-surface rounded-t-2xl shadow-2xl max-h-[70vh] flex flex-col animate-slide-up"
+      >
+        {/* Handle */}
+        <div className="flex justify-center pt-2 pb-1 shrink-0">
+          <div className="w-10 h-1 bg-gray-300 dark:bg-gray-600 rounded-full" />
+        </div>
+
+        {/* Header */}
+        <div className="flex items-center justify-between px-4 py-2 border-b border-gray-100 dark:border-gray-800 shrink-0">
+          <h3 className="font-bold text-base text-gray-900 dark:text-gray-100">{title}</h3>
+          <button onClick={onClose} className="p-1 text-gray-400 hover:text-gray-600">
+            <Icon name="close" size={20} />
+          </button>
+        </div>
+
+        {/* Options */}
+        <div className="flex-1 overflow-y-auto overscroll-contain pb-safe">
+          {/* 전체(초기화) */}
+          <button
+            onClick={() => handleSelect("")}
+            className={`w-full text-left px-4 py-3 flex items-center justify-between border-b border-gray-50 dark:border-gray-800/50 ${
+              !value ? "text-brand-600 dark:text-brand-400 font-medium bg-brand-50/50 dark:bg-brand-900/20" : "text-gray-700 dark:text-gray-300"
+            }`}
+          >
+            <span>전체</span>
+            {!value && <Icon name="check" size={18} className="text-brand-500" />}
+          </button>
+
+          {groups.map((group) => (
+            <div key={group}>
+              {group && (
+                <div className="px-4 py-2 text-[11px] font-semibold text-gray-400 dark:text-gray-500 uppercase tracking-wider bg-gray-50 dark:bg-gray-800/50 sticky top-0">
+                  {group}
+                </div>
+              )}
+              {grouped[group].map((opt) => (
+                <button
+                  key={opt.value}
+                  onClick={() => handleSelect(opt.value)}
+                  className={`w-full text-left px-4 py-3 flex items-center justify-between border-b border-gray-50 dark:border-gray-800/50 active:bg-gray-100 dark:active:bg-gray-800 ${
+                    value === opt.value
+                      ? "text-brand-600 dark:text-brand-400 font-medium bg-brand-50/50 dark:bg-brand-900/20"
+                      : "text-gray-700 dark:text-gray-300"
+                  }`}
+                >
+                  <span className="text-sm">{opt.label}</span>
+                  {value === opt.value && <Icon name="check" size={18} className="text-brand-500" />}
+                </button>
+              ))}
+            </div>
+          ))}
+        </div>
+      </div>
+    </>
+  );
+}