Any service like Briar that wants to sit atop base smartphones will need to deal with this tension. A fallback is to poll intermittently for new messages, which when tuned correctly can indeed be fairly battery life forward. Of course then your messaging experience is lower bounded by your refresh interval. Modern smartphone OSes also will ruthlessly cut long-running connections in the face of power-save events on device.
In general I think an external radio that you connect your smartphone to via Bluetooth, like Meshcore or Meshtastic, is a better experience overall than simply using a smartphone. Dedicated radios keep smartphone batteries topped up, and having the option to setup an antenna means that if you happen to be in an area where permanent radio setup is plausible, you can lean on good site characteristics, antennas, and filters. It’s hard for a government to ban radios altogether and ISM-ish band devices have a variety of uses in pretty much any developing or developed country (often used in small things like meters or monitors.) And for folks who just some off-grid data capabilities, this approach offers high flexibility without the burden of licensing.
For folks considering going into this, I suggest joining Meshtastic or Amateur Radio communities. I find the further you get from amateur radio or networking communities (mesh* communities have a mix of folks and some can have pretty poor understanding of how radios work), the more the information becomes unreliable and more suffuse with political/social goals than matters like understanding signal propagation or congestion. If you’re in a developed country, Amazon likely has all you need to get started with the Mesh* world of LoRa UHF radios.