To get a 90-minute recording into a 2 GB file size requires a bitrate of about 3 Mb/s. Even the lowest quality ProRes setting the HyperDeck Studio Mini can record, which is ProRes Proxy requires 18 Mb/s for 720p24 video. Which would work out to 12 GB for a 90 minute video.
There is a list of target data rates for various resolutions and ProRes levels in the Appendix of the ProRes white paper:
https://images.apple.com/final-cut-pro/ ... _Paper.pdfProRes was really designed as a intermediate codec for editing (hence the higher bitrates to preserve quality). If you need lower bitrates, I would look at a distribution codec like H.264. With H.264 a bitrate of 3 Mb/s for 720p is certainly possible. And recording the H.264 encoded output of OBS is certainly one way to do this.
Also, unless the 24fps output is a strict requirement, I would probably suggest down-converting to 720p30 which is simpler conversion with less potential for motion artifacts. Converting from 60 fps to 24 fps requires either dropping frames at irregular intervals (dropping one frame then two frames, then one, then two and so on) or a more sophisticated frame blending approach.
In contrast, the 60 fps to 30 fps conversion is much simpler, just drop every other frame. So in terms of motion things will end up looking a little closer to the original.