Going into low-power mode and then being woken up by the tower is standard function (even of 4G) - it's called paging, and pretty much all devices support it.

Unfortunately, although listening for these paging messages requires less power than having a full connection, it's still non-zero.

For really lower-power applications, 5G (and I think some of the later 4G extensions) support Mobile-Initiated Connection Only, which essentially means the device goes into low-power mode but doesn't even listen for paging messages - instead, it wakes up occasionally (maybe even just once a day) and sends and receives messages. The tower knows to not even bother trying to page it.