your question does not make sense, I don' t think... the following is not an answer, only some context to assist as you continue your research
Can you record directly on the R5C? of course
Can you use those recordings within OBS Studio or other video editor/compositing software? of course
Does the R5C output log/RAW over USB? sure, Internal Recording is more limited.
However, I believe this is more a case of the camera writring to an external storage device (ie writing a file, just externally, not internally)... I think... don't take my comment as authoritative... and down the rabbit whole I go... looks like I was wrong
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Ok, appears external recorders are capturing and the re-encoding HDMI video... uh, ok... hmmm... weird... anyway
So, what you will need is a 'capture card' (legacy name, really a HDMI to USB adapter) .. and first requirement will be making sure that adapter can support the video resolution, bit depth, etc that you plan to use
Then, assuming you can get the HDMI video input from camera to Operating System (has nothing to do with OBS Studio), then next step (per your question) is setting the Recording format.
- What is your use case? avoid cost of ATOMOS? or ?? I ask as that will help guide answer(s)
- Is CLOG a standard supported format in OBS Studio to Record to? no.... however, with FFmpeg you have all sorts of encoding options (all at your own risk). With that said, typically, real-time video encoding is VERY computationally demanding, and often the desire is for GPU encode offload (so as to not overwhelm CPU).
I suspect your answer will be within the options available to FFmpeg for encoding. which isn't something I'm familiar with, so I'll let others comment
Good Luck, and now I'm curious... I'll be watching this thread. Seems overly complicated to use an external recorder, though I'm sure there are specific use cases where it makes sense