It’s fine it’s a dumb display, I’m just surprised i can’t just make a socket connection and push some packets into the display over lan. It’s not just “server” software, there’s a full legit web app sitting in the middle.
Listening on a port (running as a server) requires that the network interface remains up at all times, consuming more battery, than a client interface where the network interface can be turned off (or put into low power mode) until the next poll event occurs.
Really depends on the cycle, from experience in a similar project, with a dedicated low-power enabled processor, then waking up, booting and connecting to network draws a lot of power. If you do that often enough you will actually loose power
The current solution offers a management interface for a fleet of such devices with different content and "renderers" and power and activity statistics and charts and an HTTP API interface.