Security
The library stays on the computer you are using. The website account stays in that browser.
On your Mac
Notes and files are kept by the app on this Mac. A privacy mode in the app is there when you want the page kept closer.
Your own model keys
If you add an OpenAI, Anthropic, or Google key in the app, that key stays on the device and is used only for your requests.
This website
Sign-in only checks the account saved in this browser. Clearing the site data, or choosing Sign out, removes that account from the browser.