CaddyVault runs entirely in your browser. The vault of archived tabs, the groups, the search index and your settings live in Chrome's local extension storage on your machine. There is no CaddyVault account and no CaddyVault server. Nothing about your tabs is sent anywhere.
Google Calendar is optional. If you connect it, the extension asks Google for read-only access to your upcoming events and uses the event titles to decide which archived tabs to bring back. The sign-in token stays in your browser. CaddyVault never writes to your calendar and never sends calendar data to anyone.
Notifications are shown by Chrome on your device, from data already on your device.
The optional session agent is off until you add your own API key or local bridge in Settings. When it is on, it sends the title of the upcoming event, your profile text and the titles of related archived tabs to the model you configured, so it can prepare a workspace. Nothing is sent before you set that up.
The walkthrough on the home page is sample data, not your tabs.
Uninstalling the extension deletes everything it stored. Questions go through the support link on the Chrome Web Store listing.