Can I roll it out to every team at once?
Once the app is installed it is available to every licensed user on the site, with nothing to switch on per team or per space.
Rules themselves are per person: each user creates their own, an administrator can create one on someone's behalf, and a connected integration creates them from its templates.
Related pages
Installation and Setup Guide - where this is covered in full.
Setup and Installation - more questions on this topic.