Your sessions, snoozed tabs and settings are stored by Chrome on your computer. Nothing is synced, and Cove has no account and no analytics.
When you click Auto-group my tabs, Cove sends the title (up to 120 characters) and the site name of each tab in that window to Cove's server, which asks an AI model provider to suggest groups. Full web addresses, page content and pinned tabs are not sent.