Sending messages to cellular IoT device options?

Hi all,
I am developing an asset tracker using a SIM7000 series module and (currently) an Arduino Nano. I am communicating with the device using SMSs. I'm thinking about developing an ios/android app, and I have a question which I think someone can answer pretty easily.

When the device wants to alert the android app, it sends a message to a server via http, no problem.

When I want to alert the device of a change, I use the android app - and here's my question... I'm guessing I have 2 options:

  1. I have the device actively connect to the server and request any new messages frequently (costs: power and data)
  2. I run a webserver on the device and the server sends messages to that webserver (costs: power? and I probably can't do this on an Arduino Nano)

The beauty of SMS is that the device "passively" receives updates I send to it. "Passively" is in quotes because obviously it's not passive, just passive in the sense that I personally don't have to write code to make this work, and it doesn't cost me any data unless there IS an SMS, it just "magically" appears on the SIM card, which I check every few seconds.

Is there any way to have this device NOT have to actively request updates from the server, and NOT run a webserver (which I kind of don't think I can do with a Nano - I'm already at 73% program space capacity). I'm a developer but not a web or app developer, so my knowledge is light in these areas.

Thanks you for any ideas-