Why can't I use the Nothing X app to connect to my Nothing Ear while on a call with an iOS device?

This is normal. When connected to an iOS device, the Bluetooth connection through the app uses the BLE (Bluetooth Low Energy) protocol. The earbuds and the app establish a connection via low-power Bluetooth. During a call, the system prioritises processing power and communication bandwidth for the call as priority. Consequently, the communication over low-power Bluetooth is halted.