The HDMI Expansion Card, like the vast majority of USB-C to HDMI adapters, only supports up to HDMI 2.0b.
HDMI 2.0b has insufficient bandwidth for what you want. In fact even at 4k 120 Hz 8 bit it is using aggressive compression to condense the data into the limited bandwidth (it is likely using 4:2:0 subsampling, which essentially means the computer is sending a full resolution black and white image and a half resolution color image that the display recombines to produce something between in quality, the reduction in quality is most noticable around text). Bandwidth is simply insufficient to achieve 10 bit even with the supported compression methods.
To achieve 4k 120 Hz 10 bit at all will require an adapter with support for HDMI 2.1 or above, and achieving it without any compression will require the adapter to communicate with the computer over DisplayPort 2.0 or above (the laptop doesn’t support HDMI, so the adapter communicates with the computer over DisplayPort and then translates it to HDMI).
Many adapters (and laptops, IDK about the FW16 specifically) are also limited to DisplayPort 1.4b from the computer, which also restricts bandwidth. Although it supports DSC (a better compression method that many people say looks just as good as no compression) so that’s not a huge issue.