I just did a fresh install to a USB3.0 thumb drive using 22.04.2 LTS and was able to get my RX 5600XT working with OpenCL. 5600XT is a Navi10, the 6700XT is a Navi22. Maybe it will work...
I grabbed the non-HME version 22.40.3 for Ubuntu 22.04.2. dpkg -i....then:
root@yada:/# amdgpu-install --usecase=workstation,rocm,opencl --opencl=rocr,legacy --vulkan=pro --accept-eula
There was a couple messages about missing firmware in /lib/firmware/amdgpu which appears to be common but they were a handful of specific code named GPU's. Looking at that directory shows a bunch of files for many types like Pitcairn, and Navi, and Vega.
Did a reboot and clinfo shows the 5600XT.
If you plan on compiling things with OpenCL support such as JTR be sure to:
sudo apt-get -y install ocl-icd-opencl-dev opencl-headers
Lastly, I added my user to groups video and render but I'm not getting any devices when I run clinfo or john --list=opencl-devices. Running as root works fine. Close enough for me.