SOLUTION: As long as you have the Arduino Extension installed (which I presume you do) then just open the Command Palette (command+shift+p on a mac) and type "Arduino: Send Text To Serial Port". This then turns the Command Palette text box into an input text box so that anything you type into it is then sent to the serial port once you hit "enter".
I'll attach a screenshot from the answer in the thread linked above (hope that's ok).
Hopefully I understood your problem correctly and this helps!
I think that this thread was about writing an applicationin Visual Studio that can communicate with the Arduino, not so much about writing an Arduino application in VS Code.
If I'm not mistaken you have to use 2 ports to do this. The Arduino port cannot support two devices on the same port. VS will have to access the data through the second serial port. You can buy a USB to TTL serial adapter module on Amazon that will handle this. Plug in the USB end to the PC and tie the TTL end to a serial port on the Arduino. This wat the VS can down load data from the Arduino with the right code on the board. What you do with the data in VS is up to you; I've never used a monitor in VS, just screens.
Good luck
man I have this same issue with the arduino plugin for vss(visual studio code). When I first installed the plugin the serial monitor worked perfectly. After a few flashes to my uno the ide froze and I restarted it and then I NEVER got serial info again. I had to get a program called Serial Port Monitor to get my serial data. Which is actually not a bad workflow especially if you have multiple monitors. The only annoying part is I have to close the communication each time I wana flash then re open after microcontroller has been flashed.
If anyone has any ideas to get serial data back into vss please let me know.
