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.

Paging goes back to the original GSM (so even before 2G). In fact, the technology of paging predates mobile voice. The technology was used in pagers!

It is a staple of any always-available battery powered device.