For the bot to work with events in your group to its full extent – publish them on its behalf with a sign-up button, promptly apply changes, and keep track of participants – it must be added to that group.
All group administrators can publish events in the group via the bot. If the bot is also made an administrator, it can keep track of changes in the admin list in real time.
When making the bot an administrator, there is no need to grant it extended permissions – they can be turned off.