A bookmark saves a page address, not your game state. Progress may depend on the browser, profile and storage method used by each game.
Check before a long session
Open 2048 Remastered or another favorite and inspect any save instructions. Do not assume that every game saves automatically or syncs between devices. If you want to test persistence, use a short disposable session, wait for any save indicator and reopen the same page in the same browser profile. A successful test confirms only that situation.
Know what can remove a save
Private browsing, clearing site data, switching profiles or changing the site's address can make local progress unavailable. Browser-managed storage may also be removed under storage pressure. Before cleanup, use an export or account feature only if the game actually provides it. Screenshots record a score but cannot restore a playable session; missing local data is not always recoverable.