refactor(api): unify /api contract across frontend, nginx, and backend

frontend/src/lib/backendVersionCache.ts

@@ -0,0 +1,21 @@
+const STORAGE_KEY = "calendar_run.backendVersion.v1";
+
+export function readCachedBackendVersion(): string | null {
+  try {
+    const raw = sessionStorage.getItem(STORAGE_KEY);
+    return raw !== null && raw.trim().length > 0 ? raw.trim() : null;
+  } catch {
+    return null;
+  }
+}
+
+export function writeCachedBackendVersion(version: string): void {
+  try {
+    if (version === "недоступна" || version === "не указана") {
+      return;
+    }
+    sessionStorage.setItem(STORAGE_KEY, version);
+  } catch {
+    // private mode / quota
+  }
+}