Using Serial Plotter with Visual Studio Code
Without very specialized software that can create two new devices with the correct "teeing" policy, it's not going to be possible.  Only one program can open a serial port at a time (certainly and have it get anything intelligible out of it...)

I would suggest you may want to add a second serial port.  Use an FT232 adaptor to communicate on another serial connection (or a SoftwareSerial connection at a pinch) for your debugging information.  You really want a board with more than one serial port for this - or a board with a native USB for programming and a hardware serial port for data communication.

Another alternative is to ditch the serial for programming altogether and program your board through a dedicated programmer, thus leaving your serial port free for data communication.