Capture One can read additional tone-mapping metadata in Apple ProRaw format, making the picture look practically identical to what you see on your Apple iPhone Pro.
The default Film Curve for newly imported ProRaws is “DNG Tone Mapped”
If the result of the tone mapping is found to have too much of an effect, it can be changed to the standard DNG Film Curve from the Base Characteristics tool. You will notice a drastic change in the overall tone of your image, so it's best to take this step first before editing ProRAW files.
ProRaws imported previously to CO 23 (16.1.0) will persist with the DNG Standard film-curve. You can select the new tone-mapping by selecting “DNG Tone Mapped” from the Base Characteristics Tool, as shown above.