Capture One doesn't have an "internal" color space because it doesn't need to. When working with an image in Capture One, it's only a preview of what the output will be. The profile of the preview is set under View > Proof Profile. It defaults to Selected Recipe (the highlighted recipe, not necessarily the enabled recipe).
It's entirely possible for the preview (and output files) to be clipped in any/all of the channels. That is a linear system to be precise.On the picture, you will find that the Base Characteristics sets the initial profiling – under Camera Profile. This is the initial translation from 0s and 1s to an image preview.
The Output Profile is next, and the Colorspace Conversion section is what takes Proof Profile value and passes it to the monitor profile, rendering the color on the display.
The readouts/histograms/etc are all based on that middle section.
NOTE: When Proof Profile is "no proof profile", it's removing that middle bit from the chart. You still have Base Characteristics mapping the 0s and 1s to a preview, but there's no additional mapping to the proof profile. What is displayed on the screen is still affected by the monitor's profile