fix(M02): 층 단추 눌린 표시 · 한 줄 폭 맞춤, 프로젝트 기본값은 마지막 고른 것 → 내 최근 것 → 빈 칸

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_0148XFUpPfpiuTjxF1EK9c95

M02_MasterTemplete/M02_MasterTemplete_UI_Page.ts

@@ -20,6 +20,7 @@ export async function renderM02MasterTemplate(root: HTMLElement): Promise<void>
   const main = createMain(isAdmin);
   const side = buildSide({
     isAdmin,
+    userName: user?.name,
     onOpen: (sel) => void main.open(sel),
     getOpen: main.current,
   });