feat(app-hub): 허브 도구 레일과 입장 동선을 정리

맥락:\n- 상단 헤더 요소가 많아 허브의 핵심 흐름(공간 선택 → 목표 입력 → 입장)이 분산되었습니다.\n- 메모/통계/설정 진입을 상단이 아닌 보조 동선으로 옮겨 감성 톤을 유지할 필요가 있었습니다.\n\n변경사항:\n- 우측 아이콘 레일과 우측 드로어를 추가해 Inbox/Stats/Settings를 동일 패턴으로 제공했습니다.\n- TopBar에서 메모 버튼을 제거하고, 멤버십/PRO 동선은 ProfileMenu 드롭다운으로 정리했습니다.\n- Selected Space 박스를 슬림화하고 설명을 1줄로 제한해 시선 분산을 줄였습니다.\n- 추천 공간 카드에 텍스트 가독성 오버레이와 선택 표시(은은한 테두리/체크)를 적용했습니다.\n- Quick Entry에서 커스텀 CTA 무게를 낮추고 전체 톤을 가볍게 조정했습니다.\n- docs/work.template.md를 추가하고 docs/work.md의 현재 작업 지시를 갱신했습니다.\n\n검증:\n- npm run build\n- npx tsc --noEmit\n\n세션-상태: /app 허브가 상단 과밀 없이 레일+드로어 보조 동선으로 정리되었습니다.\n세션-다음: 드로어 패널의 실제 데이터 연결 시 도메인 상태와 연동을 진행합니다.\n세션-리스크: 드로어 포커스 트랩/키보드 동선은 추가 접근성 점검이 필요합니다.

src/features/profile-menu/ui/ProfileMenu.tsx

@@ -1,12 +1,20 @@
 import type { ViewerProfile } from '@/entities/user';
 import { Dropdown, DropdownItem } from '@/shared/ui';
+import { cn } from '@/shared/lib/cn';
 
 interface ProfileMenuProps {
   user: ViewerProfile;
   onLogout: () => void;
+  onOpenBilling?: () => void;
 }
 
-export const ProfileMenu = ({ user, onLogout }: ProfileMenuProps) => {
+const MEMBERSHIP_LABEL_MAP: Record<ViewerProfile['membershipTier'], string> = {
+  pro: 'PRO MEMBER',
+  normal: 'NORMAL',
+  team: 'TEAM',
+};
+
+export const ProfileMenu = ({ user, onLogout, onOpenBilling }: ProfileMenuProps) => {
   return (
     <Dropdown
       align="right"
@@ -21,6 +29,20 @@ export const ProfileMenu = ({ user, onLogout }: ProfileMenuProps) => {
         </span>
       }
     >
+      <div className="rounded-lg px-3 py-2">
+        <p className="text-[11px] uppercase tracking-[0.14em] text-white/48">Membership</p>
+        <p
+          className={cn(
+            'mt-1 text-xs font-medium',
+            user.membershipTier === 'pro' ? 'text-amber-200/88' : 'text-white/80',
+          )}
+        >
+          {MEMBERSHIP_LABEL_MAP[user.membershipTier]}
+        </p>
+      </div>
+      {onOpenBilling ? (
+        <DropdownItem onClick={onOpenBilling}>PRO 기능 보기</DropdownItem>
+      ) : null}
       <DropdownItem href="/stats">Stats</DropdownItem>
       <DropdownItem href="/settings">Settings</DropdownItem>
       <DropdownItem danger onClick={onLogout}>

src/features/room-select/ui/RoomPreviewCard.tsx

@@ -31,10 +31,16 @@ export const RoomPreviewCard = ({
         compact
           ? 'h-[98px] min-w-[152px] snap-start p-2 sm:min-w-0 sm:aspect-[5/4]'
           : 'h-[292px] p-3 sm:h-[334px] sm:p-4 lg:h-[356px]',
+        compact &&
+          'after:pointer-events-none after:absolute after:inset-x-0 after:bottom-0 after:h-[62%] after:bg-[linear-gradient(to_top,rgba(2,6,23,0.88),rgba(2,6,23,0.34),rgba(2,6,23,0))]',
         selected
-          ? cinematic
-            ? 'border-sky-200/44 shadow-[0_0_0_1px_rgba(186,230,253,0.34),0_20px_50px_rgba(2,6,23,0.32)]'
-            : 'border-brand-dark/28 shadow-[0_0_0_1px_rgba(48,77,109,0.18),0_16px_40px_rgba(15,23,42,0.16)]'
+          ? compact
+            ? cinematic
+              ? 'border-sky-200/54 shadow-[0_0_0_1px_rgba(186,230,253,0.36),0_0_20px_rgba(125,211,252,0.22)]'
+              : 'border-brand-dark/32 shadow-[0_0_0_1px_rgba(48,77,109,0.22),0_0_16px_rgba(99,173,242,0.18)]'
+            : cinematic
+              ? 'border-sky-200/44 shadow-[0_0_0_1px_rgba(186,230,253,0.34),0_20px_50px_rgba(2,6,23,0.32)]'
+              : 'border-brand-dark/28 shadow-[0_0_0_1px_rgba(48,77,109,0.18),0_16px_40px_rgba(15,23,42,0.16)]'
           : cinematic
             ? 'border-white/16 hover:border-white/28'
             : 'border-brand-dark/16 hover:border-brand-dark/26',
@@ -73,20 +79,33 @@ export const RoomPreviewCard = ({
         )}
       >
         {selected ? (
-          <span
-            className={cn(
-              'absolute left-3 top-3 inline-flex items-center rounded-full border px-2 py-1 text-[10px] font-medium',
-              cinematic
-                ? 'border-white/26 bg-slate-950/42 text-white/78'
-                : 'border-white/52 bg-white/70 text-brand-dark/74',
-            )}
-          >
-            선택됨
-          </span>
+          compact ? (
+            <span
+              className={cn(
+                'absolute right-2.5 top-2.5 inline-flex h-5 w-5 items-center justify-center rounded-full border text-[11px] font-semibold',
+                cinematic
+                  ? 'border-sky-200/64 bg-sky-200/26 text-sky-50'
+                  : 'border-brand-primary/52 bg-brand-primary/18 text-brand-primary',
+              )}
+            >
+              ✓
+            </span>
+          ) : (
+            <span
+              className={cn(
+                'absolute left-3 top-3 inline-flex items-center rounded-full border px-2 py-1 text-[10px] font-medium',
+                cinematic
+                  ? 'border-white/26 bg-slate-950/42 text-white/78'
+                  : 'border-white/52 bg-white/70 text-brand-dark/74',
+              )}
+            >
+              선택됨
+            </span>
+          )
         ) : null}
 
         {compact ? (
-          <div className="w-full rounded-lg bg-slate-950/44 px-2 py-1.5">
+          <div className="w-full rounded-lg bg-[linear-gradient(180deg,rgba(2,6,23,0.28)_0%,rgba(2,6,23,0.58)_100%)] px-2 py-1.5">
             <p className="truncate text-sm font-semibold text-white">{room.name}</p>
             <p className="mt-0.5 truncate text-[11px] text-white/70">{room.vibeLabel}</p>
           </div>