You have several INTEL GPUs.

[aspizu]

Using locale en_US
DaVinci Resolve checker 3.0.0
Installed DaVinci Resolve package: 
Chassis type: Convertible
Installed OpenCL drivers: intel-compute-runtime
Presented GPUs:
        Alder Lake-P Integrated Graphics Controller (kernel driver in use: i915)
        DG2 [Arc A370M] (kernel driver in use: i915)
OpenGL vendor string: Intel
OpenGL renderer string: Mesa Intel(R) Graphics (ADL GT2)

You have several INTEL GPUs. I am confused. Are you using multi-cpu desktop motherboard? Or intel igpu + intel dgpu (which does not exist at the moment of writing)?

[tippfehlr]

I love these error messages :) Greetings from 2023, Intel Arc exists now xD

Not actually helping, sorry

[Ashark]

I guess it is still impossible to use intel only. At least igpu. As I remember, intel's opencl implementation lacks some functions that are needed for DR. But things could be changed now. Can you please test if it is possible to run DR with intel dgpu/igpu?