Another anomaly is the FPGA DONE LED is off. The ARTIQ/SZL firmware is supposed to configure the FPGA and that LED would turn on.
Did you check all power supply voltages?
Did you set the correct baud rate? 115200-8-N-1.
You don't need PuTTY, you can simply do:
stty 115200 < /dev/ttyUSB2
cat /dev/ttyUSB2
Unplug and replug the USB cable to reset the USB UART, PuTTY may have selected some options you do not want. Also make sure programs like ModemManager are not interfering.
If you cannot make progress with the serial port, then you need to use a JTAG debugger (OpenOCD and such).