From my reading it seems that Resolve runs fine on Linux with the exception of some codecs not being available.
My biggest concern is with playing footage inside of Resovle (I think the codec issue might affect this as well). My Sony A7IV records footage at 4k h264 (10 bit 4:2:2), the free version in Windows doesn’t playback this footage at all. MacOS doesn’t have this issue at all.
I’m assuming I’ll need to transcode my footage with ffmpeg on Linux the same as I do on Windows. Is that correct?
H264 or mp4 file format is proprietary and requires a license. Windows includes the license thus why mp4's work but Linux doesn't include them outside of the Pro version.
Ffmpeg or handbrake can convert your video files to another encoding format that works.
The Arch wiki goes over troubleshooting tips https://wiki.archlinux.org/title/DaVinci_Resolve#Troubleshooting