The free version has h264 and h265, as far as I can tell. I rendered a mp4, h264 video in resolve today. My first time using the software and it was surprisingly capable. (I needed to blur a moving face in a video)

Not in Linux, only in Mac and Windows

On Mac and Windows, the free version of Resolve supports H.264 and H.265 (using OS-supplied codecs IIRC).

Linux H.264 and H.265 support is Studio-only[1] (presumably because royalties).

If you don't care about any other Studio features, converting to/from an intermediate codec — DNxH[DR], say — on import/export using another tool like FFmpeg seems like a reasonable workaround for most applications.

Since Resolve doesn't support H.264/H.265 passthrough (on any platform), the only generation loss added by this approach will be from DNxH[DR] encoding, which, assuming a sufficiently high bitrate for the intermediate codec, should be minimal.

Note that even Resolve Studio doesn't support AAC audio on Linux[2], so, for many H.264/H.265 projects, you'd end up with pre-/post-conversion steps even if the video codecs were supported.

[1] https://documents.blackmagicdesign.com/SupportNotes/DaVinci_...

[2] https://documents.blackmagicdesign.com/SupportNotes/DaVinci_...