The snag is that via App Inventor Apps, Arduino is the most popular microcontroller family to work with, hence there is very little information about working with AI and Pi.
When an App Inventor App sends data via BT, how that data is collected and processed is entirely covered by the micro-controller's Script (known as a Sketch in the Arduino world).
If as you say, you have verified that a BT connection has been made, then the data ("C") should reach the Pi, but you have actually not got a connection.
There is a flaw in your App code where you have the [ListPicker Selection] being set by the [call BluetoothClient] function.
I attach a basic example Project that should prove if there is a connection and if so send text data ("Hello") on button click. I suggest you try this (change "Hello" to "C") and see if the Pi receives the data. If it does, you can modify the example as required or copy Blocks from it into your own Project (via the BackPack).
BT_Basic_Setup_Send.aia (7.1 KB)