Update TypeScript and types packages

This pulls in TypeScript 4.4, which ships ResizeObserver in the DOM
types, as well as sets caught errors to `unknown`, requiring explicit
checks for `AbortError`.

src/shared/prerendered-app/Intro/missing-types.d.ts

@@ -30,11 +30,6 @@ interface WindowEventMap {
   beforeinstallprompt: BeforeInstallPromptEvent;
 }
 
-interface ClipboardItem {
-  types: string[];
-  getType(type: string): Promise<Blob>;
-}
-
 interface Clipboard {
   read(): Promise<ClipboardItem[]>;
 }