A useful distinction
Progress stored in a browser can be affected by data clearing, browsing context or the game’s implementation. A new browser profile may not contain the same local record. These possibilities need the actual game’s saving behaviour to be understood.
Put it into practice
Keep local storage, an export file and an account-based save conceptually separate. Read the published saving instructions before changing profiles or settings. For your own prototype, test with disposable data and document the limitations clearly instead of presenting a local record as a permanent backup.