Optiplex 5060 SFF unable to get 4K resolution

Did you adjust the settings in Windows:

Go to Settings → System → Display → Advanced display settings, and adjust the resolution.

Tried that, same results.

Re: Displayport/Displayport yields no video at all

5060 SFF has two DP 1.2 video ports.  If you use a straight DP to DP cable and cannot get any video from either port, you need to verify the DP cable and monitor (in DP mode) both work using another DP video source.  UHD620 or 630 can only support 4k @ 60Hz at DP.  Also 5060SFF cpu should have UHD630, not 620.  620 is used in mobile cpu only (e.g., i7-8550U) which requires a different socket.  Was it a typo?  Do you actually mean UHD 630?

Converting DP to hdmi is not as straightforward as it sounds.  The conversion adapter must be directly connected to the DP video source receptacle without a cable.  You need an active DP to hdmi adapter because 5060 DP out is not dual mode (DP++ logo). 

When the GPU detects an HDMI adapter, it will send an HDMI signal instead of a DisplayPort signal. The pins of the DisplayPort will be mapped to the HDMI pins. Keep in mind, though, that this will only work for 1080p or lower resolution.  Therefore you cannot achieve 4k hdmi by converting from DP.

https://nerdtechy.com/active-passive-displayport-difference

uhd 620 / UHD 630

• Max Resolution (HDMI)4096 x 2304@24Hz
• Max Resolution (DP)4096 x 2304@60Hz

My Samsung UHD S70A S32A70 has both DP and HDMI inputs. Trying the 5060 DP port to monitor DP port yields no video from either 5060 DP port with a male to male DP cable. I am awaiting delivery on eBay # 224741520830 cable to try the DP to HDMI conversion. The DP to HDMI port converter I have is not rated to 3840 x 2160. The new cable is supposed to be rated at 3840 x 2160. It is supposed to be here in a few days.

Yes it is Intel UHD Graphics 630 I have loaded. Having said that, shouldn't the available resolutions be listed, even thought they might not be able to be displayed properly?

if monitor is set to refresh at 60 hz, only straight DP from 5060 without conversion can support 4k.  if DP does not give video, something wrong with DP-DP cable, monitor DP in, or PC DP out.    if you use HDMI adapter, pc will tell you what resolution is available.  it seems DP to HDMI can only go up to 1080p.  this is consistent with your report "I am unable to get a choice higher than 1920x1080".

I tried another male/male DP cable, same results. I called Samsung service. They said if the monitor has a DP and HDMI jack on the back, it is for U.K. market. Don't know it is is true or not. But, the straight thru DP cable does not work at all. I think I'll return it, and try another manufacturers UHD monitor.

Does this LG look like a reasonable candidate? LG 32UD59-B

not familiar with 4k monitor review.  if I understand your issue correctly seems your Dell pc DP does have positive DP video output which you converted to HDMI albeit at lower resolution.  It is just you do not have a verified working 4k DP monitor to test the native DP video signal resolution directly without any conversion, assuming you have good quality DP to DP cable.

If I cannot get the onboard DP port to 4K resolution, might this be an alternative graphics card? eBay #165161578389

you would still need a working 4k monitor and good quality DP-DP cable for this card.  this Dell R5 430 card supports 4k video from DP only without conversion.

your onboard DP is supposed to support 4k.  no matter what the actual DP signal resolution is on your sff, you said the integrated DP port gives positive video signal (it can produce hdmi signal via adapter).  Then when you connect that positive DP signal to your DP-DP cable and connect to monitor, you get no video, it tells you the problem is downstream from pc, either in the cable or monitor, but not the pc DP itself (no matter what resolution it has).  I suspect your monitor is the source of issue.  try another monitor (does not have to be 4k) that has DP in.

A new different mfg. monitor (LG) arrived last night. Selected DP input on the display menu, plugged in DP to DP, and all is well. Apparently the DP input was faulty on the Samsung. Thank you for all you assistance and final resolution :).