@jwdrone  The "Asmedia USB Host Controller was not found" error is likely because the XPS 8950 doesn't use that USB controller. Look in Device Manager to see what USB controller is listed, eg Intel USB3.1 and/or USB3.2.

Do both of your NVME SSDs work?  Don't know if having 2 NVME SSDs can cause a problem for the x4 PCI-e slot. As a test, you could remove the 2nd (non-boot) SSD and see if the card works in the x4 slot now. But, I suspect you'll still get the Asmedia error message...

Is the Startech card compatible with Win 11?  You may want to contact Startech tech support to see if their card requires the Asmedia USB controller and/or if there's a workaround.

All of my NVMe slots are full and I have an X 1 sound card in one of the X 4 slots and it works.

I have a few updates.  My 8950 has an Intel USB3.20 extensible controller that shows up in device manager.  The Startech card has an ASmedia controller and that's what the software is trying to update.  It can't because that controller is not recognized in device manager.

My SSD's and network adapter work fine.  kras2 posted that they had 3 NVMe slots filled and the x4 slot was operable.  I didn't try removing my SSD at this point.

Startech claims that they are Win 11 compatible and the problem is because the 8950 does not recognize the device in the x4 slot.  They also mentioned that the ASmedia controller is on the board.  They suggested that I try the board in another machine.

The closest thing I have to test the board is an XPS 8500 running Windows 10.  It has (3) x1 and (1) x16 slot.  I removed the video card and plugged the Startech card into the x16 slot.  Voila, the machine booted and the card was visible in device manager as an ASmedia controller along with the two Intel USB3.0 controllers already internal.  All of the card ports worked fine.  The windows driver was correct.

So....back to the 8950.  I took out the video card and installed the card in the x16 slot.  Lovely blue screen with multiple restarts but never a boot.  I took the card out and the machine booted fine into Win 11.  Put the card back into each x4 slot and nothing in device manager.

I'm pretty sure it's not the card but some strange configuration in the Dell BIOS or two bad slots.  BTW the x16 works fine with the video card.  I don't have another x4 card to try but I guess that's the next step.  As near as I can tell the 8950 should still be under warranty but because I bought it used and don't have the original receipt, Dell service techs won't talk to me.

Any other ideas?

Have you tried turning off secure boot?

Also running UEFI/BIOS revision 1.9.1

My specs are similar to yours. 12700k CPU, 2 SSD's in the NVMe slots and a killer wireless in the third, 32Gb of ram and a 3060Ti video card. 

@jwdrone   - Glad you found a card that works!

Wonder if this one is working because you're using the (optional) SATA power connection? Will it still work if you disconnect the extra power connection? 

If it only works with the SATA connection, that suggests the x4 slot isn't providing enough power, and that might also explain why the other cards you tried, which didn't have SATA power, didn't work...

Yes.  It shows up in device manager without the power attached.  I didn't try multiple devices to see power output etc.  The previous card also had optional power which I used but it never showed up in device manager.  The previous card had a ASMedia - ASM3142 and a Genesys Logic - GL3590 controller.  This one has only ASMedia.  Startech believes Dell is not compatible with Genesys.

@johnblaustein  Good news! 

Getting this information from Dell is like pulling teeth! But I finally got an answer! For The XPS 8950 you can get a 3.5 inch PCIe x4, x8 or x16 for those who are trying to add a USB expansion. If I may add this link.