How much bandwidth roughly does Esper use while idle? (Not including remote viewing or changing of compliance policies.)
Esper consumes about 5MB of total data a day. As you note, other activities you fire through Esper will of course consumer bandwidth, a big one being installing apps to your devices or pushing out files using the Content Management feature.
We do get queries about high data usage from time-to-time, when we've dug into those they are typically updates to Google Play libraries on GMS devices or system updates that are pushed out by the OEM. We don't control when Google Play updates, and you have some control over system updates but ultimately it is up to Google and the OEM respectively as to when these happen.
Also note that if you are using Google Play apps, Google Play itself is responsible for pushing out any app updates from the app maker that have been posted to Google Play - this of course also impacts data usage.