Welcome to the forum @tjb 
Maybe you have to set a HSA override like so:
export HSA_OVERRIDE_GFX_VERSION=11.0.0
Just type it into your terminal every time you want to use DaVinci Resolve.
I seem to have lost my resource to find the required version for any given GPU, but I know it is 11.0.0 for RDNA3 and 10.3.0 for RDNA2.
It really becomes harder each day to find something on the interwebs.
Also in case you still want to use the open source drivers for normal use, have a look at my cookbook for ROCm 
PS: I don’t use DaVinci resolve, so I can’t really help you any further if the problem still persists.
PPS: I deleted my previous post because of a wrong link.
Good luck!