It is one screen in the app, it takes effect immediately, and there is no hold period afterwards.
Settings → Account → Delete account. You will be
asked to type the word delete, because this cannot be undone.
All of it goes at once. Nothing is kept for a grace period, and there is no copy to restore from afterwards.
Books stored on your own device. Those are your files in your own folders, and closing a cloud account is not a reason for this app to go through your storage. Uninstalling removes any copy the app made for itself.
Reinstall and sign in once to reach the button, or write to the address below and ask — say which email address the account uses.
This deployment has not published a contact address. The operator sets SYNKITAB_CONTACT_EMAIL to fill this in.