The adapters you have should work, but there are sometimes some tricks to seeing it actually succeed (depending on adapter design and USB chipset). If the chipset is FTDI it should probably “just work” without most of the “tricks”.
Sometimes the USB portion is powered by the device, and at other times by the host. It may be necessary to unplug and replug one end or the other after power is actually up. Order of powering up device and host may change things. “lsusb” should at least show the adapter on the host.
Once it is connected you need to use a serial console program, e.g., minicom, gtkterm (my favorite), or PuTTY. Finding the right serial device can be a pain, especially under Windows. Once you have this running, speed is 115200, 8 bits, no parity, 1 stop bit. Typically flow control with a full DB-9 connector is RTS/CTS, although software flow control would probably work as well.
If everything is set up on host, and Jetson does not show anything, keep the Jetson on, replug the DB-9, and then power cycle the Jetson while the DB-9 stays connected. If lsusb does not show the device on host, unplug and replug it on the host…after that you may still need to unplug and replug the DB-9 if host side had not been visible before.