feat(view): project save/open, Ctrl+S, save status, IndexedDB auto-backup (plan B2–B5)

- 저장 (Ctrl+S) downloads <교량명>_교각설계.pzr.json; 프로젝트 열기 reads it
  back and regenerates every pier without the source workbook.
- Save status in the header: 저장 전 / 변경 있음 · 미저장 / 저장됨. The
  snapshot excludes the history so a save is not counted as a change.
- Auto-backup to IndexedDB 0.8 s after changes while unsaved; on start a banner
  offers recovery or discard. Storage failures are reported, not fatal.
- beforeunload warns while there are unsaved changes.
- B1 (default-vs-changed tracking) is not added yet: inputs are not editable
  until the 2단계 input cards exist.
- Not verified in a browser (no debuggable Chrome in this session).

Co-Authored-By: Claude Haiku 5.5 <noreply@anthropic.com>

src/view/backup.ts

@@ -0,0 +1,53 @@
+/**
+ * Browser auto-backup in IndexedDB (spec §8, plan B4). Only the latest project text is kept.
+ * Every call can fail (private window, blocked storage); callers catch and show the failure.
+ */
+const DB_NAME = 'pierzainer';
+const STORE = 'backup';
+const KEY = 'current';
+
+export interface Backup {
+  text: string;
+  at: string;
+}
+
+function openDb(): Promise<IDBDatabase> {
+  return new Promise((resolve, reject) => {
+    const req = indexedDB.open(DB_NAME, 1);
+    req.onupgradeneeded = () => req.result.createObjectStore(STORE);
+    req.onsuccess = () => resolve(req.result);
+    req.onerror = () => reject(req.error);
+  });
+}
+
+function run<T>(mode: IDBTransactionMode, action: (store: IDBObjectStore) => IDBRequest<T>): Promise<T> {
+  return openDb().then(
+    (db) =>
+      new Promise<T>((resolve, reject) => {
+        const tx = db.transaction(STORE, mode);
+        const req = action(tx.objectStore(STORE));
+        tx.oncomplete = () => {
+          db.close();
+          resolve(req.result);
+        };
+        tx.onerror = () => {
+          db.close();
+          reject(tx.error);
+        };
+      }),
+  );
+}
+
+export function writeBackup(text: string): Promise<unknown> {
+  const value: Backup = { text, at: new Date().toISOString() };
+  return run('readwrite', (store) => store.put(value, KEY));
+}
+
+export async function readBackup(): Promise<Backup | null> {
+  const value = await run<Backup | undefined>('readonly', (store) => store.get(KEY));
+  return value ?? null;
+}
+
+export function clearBackup(): Promise<unknown> {
+  return run('readwrite', (store) => store.delete(KEY));
+}