By default, user data, including the tokens associated with all the accounts added, are stored in the extension's local storage. By default, data isn't synced across devices you use this extension on. It is only synced once you press the "Sync" button in the account manager. Your data is not automatically shared with any website outside of this extension. It is only passed to a supported website once you click "Switch to selected account on site" in the account manager while on a supported website. Your data is not sold to any data brokers. For more information about how your Rotur account data is handled outside of this addon (even when it's not installed or in use), see https://rotur.dev/privacy-policy

On top of that, your data is not used in the background while the extension appears to not be running. The developers of this extension can't see your account tokens nor your passwords or password hashes.