Hello there,
Your project looks like a very interesting one.
I have some notes/questions on it:
1) Do you want to have a full size display on the card, say your card is a 3.5" x 2.0", so should the display be of similar size? I think yes, the card will look very nice in this case.
2) Obviously it is a battery powered devices. What is the estimated discharge time. The battery will be the second largest component after the display? Important question! How to charge the battery?
3) Some low cost, but reliable ICs can be used for this project, like the same ESP32, ESP8266 or others.
4) Where located the server? On internet or in local network?
5) Supposedly the connection between the card and server must be a secure TLS based connection.
6) How to set the Wi-Fi network information like SSID and password to the devices? Using Ad-hoc network or connect to a PC via USB to set the settings?
7) do you planning to launch the device on market? if yes, you will need some certified wi-fi modules to simplify the further device certification.
Write me here if you want to discuss this or other questions.
Have a nice day!