My Moto Z Play has a 3,500 mAh battery and is rated to last 50 hours on a charge. That would net a 70 mA average draw. My usage is averaging 105 mA with a runtime of 33.2 hours.
the goTenna Mesh has a 589 mAh battery, so to achieve its rated 24-hour battery life, that means average current draw is 24 mA assuming the batttery is at 100% rated capacity. Looking at the Bluetooth transceiver spec sheet, its rated max current draw is 80 mA. The goTenna connects using Bluetooth Low-Energy, so I doubt it actually draws that much in this use case. The ARM processor draws 30-185 mA based on load when active.
So, given these current ratings, I’d say the goTenna already spends a decent amount of time in sleep mode, at least as much as it can and stay connected.