The Device Manager probably says it is an F200 because at that point they had not settled on the final SR300 name.
The problems that you are having may not be related to the camera's ID though. RealSense cameras have a history of problems when used with Surface Books and Surface Pros.
In your desktop, the E5 2658 v3 processor is a Xeon class chip with a 4th generation "Haswell" type architecture. The SR300's minimum processor requirement is a 6th generation "Skylake" processor. Whilst Xeon processors tend to defy the minimum spec and have worked with 5th generation PCs, I can only recall two cases where the SR300 has have worked with Xeon PCs as far back as 4th generation Haswell.
I believe error code -4 is related to a problem with the RealSense firmware driver. You are only the second F250 owner I have heard of (the first being the one that you linked to above), so it is difficult to diagnose a solution, because the Device Manager is treating the camera like an F200 but the hardware inside the camera is that of a SR300. Presumably the camera must have once worked though during its pre-release status as the F250.
In that case of the first F250 owner, I too read in those release notes that the F250 could use the DCM version intel_rs_dcm_sr300_188.8.131.5218.exe
Though the RealSense download page no longer lists that old SR300 DCM, I managed to track down an Intel support page where it is still available, and the download link works. It is the bottom link in the side-bar.
I apologize for misunderstanding that you had tried that particular driver.
If you are using a RealSense camera on a PC that meets its minimum specification then usually a camera detection error such as this one occurs because the PC's USB port is not reliably supplying the camera with the power that it needs. Not all PC USB ports are made equal, and so a camera may work on the USB ports of one machine but not another.
In many cases, this issue has been instantly fixed by plugging the camera into a mains-powered USB hub instead of directly into the PC. These can be found on stores such as Amazon for around $15 by searching for 'powered usb 3.0 hub'.
It's not so much a case of maximum available power as the reliability of power, and fluctuations that can cause the camera's signal to drop. A mains powered USB eliminates these fluctuations, making the camera consistently detectable. I can understand if you wish to continue exploring other options though.
This message was posted on behalf of Intel Corporation
Thank you for your patience. That seems like a very old model of the camera, before the SR300 was officially released. We suggest you to return this camera to its place of purchase and get a new SR300.
The Hardware ID of the new camera is vid_8086&pid_0aa5 and the sticker should say SR300 camera. The drivers are not recognizing that hardware ID, 0A95.
I hope you find this information useful.