Make sure you install the Intel OpenCL Compute Runtime. I’m running Mint and after installing the “intel-opencl-icd” package I was able to launch Resolve. The package name for Manjaro is probably “intel-compute-runtime” based on the Arch wiki. I’ve not run Manjaro before so I can’t any help for that distro. https://wiki.archlinux.org/title/GPGPU
I had a similar issue with DaVinci Resolve 18.6 on Kubuntu 22.04. My AMD Ryzen 7 7840U with Radeon 780M Graphics wasn’t recognized. Initially, clinfo showed no platforms. After installing the OpenCL package with:
sudo apt install mesa-opencl-icd
clinfo displayed the correct information, and DaVinci Resolve recognized my GPU. Everything worked perfectly after that.