Hi, @Nokhysh
Please check my previous reply, there is a photo showing how to connect USB to UART adapter with FRDM-RW612.
And you can input command in UART1: this port is directly connected with TYPE-C cable with your PC. And also you are using J-LINK Commander with this port. With this port, you can see ">", and also using this port to input "matterfactoryreset" command.
You can see outputs in UART2: this port is connecting to USB-TO-UART with dupont line, then connect to your PC.
I paster the photo here again for your reference.
USB-TO-UART side: FRDM-RW612 side:
VCC-------------------J5 PWM
TX ---------------------RX
RX----------------------TX
GND--------------------GND

If still there is no any output in UART2 port, you can reset FRDM-RW612 board by pressing SW1 button(Reset Button).
After reset board, if still failed, you can have a try with my .srec file. It can help you to check whether the issue is from your compiling side, or from connecting side.
Also, after successfully commissioning with chip-tool, is it possible to debug the source code to check its behavior?
==>The examples are given for your reference, and you build it on WSL or Linux, so if you want to debug, it is better to use MCUxpresso for VS code or directly use MCUXpresso like the link you paste.
Best regards,
Christine.