Your session lives in Settings → Account. There you can see which Can Do account you logged in with and you can switch accounts or sign out.
Switch Account
Use Switch Account to log in with another Can Do account. Companion opens the browser so you can sign in and then updates your projects.
Sign Out
Use Sign Out to log out. The app returns to the welcome screen and your folders stop showing in Finder until you log back in. Nothing is deleted in Basecamp.
📎 [Placeholder: screenshot — Settings → Account with Switch Account / Sign Out]
Note: when you log in you see all Basecamp accounts that your Can Do identity has access to, without connecting each one separately.
Note: after you click Authorize in the browser, the browser tab stays open on Basecamp's page rather than closing itself — that's expected. Companion has already signed you in by then, so you can just switch back to it.