External Display not displaying full OSD function tech said solution is HDMI Adapter?
Your cable has nothing to do with the features of the monitor.   What the store employee told you was utter nonsense.  

It simply can’t influence the OSD functionality of the monitor as there’s no logic in a cable that will enable it.  What does influence the OSD is the “mode” that the display is in and that’s dependent on how you have things configured.

In fact, speaking of configurations, the (cable) configuration you had previously, going from mini DisplayPort to Display port (mDP to DP) was better than going from mDP to HDMI as there’s no conversion of the signal.  You’ll get a more stable and reliable connection.

That aside, the monitor’s features are dependent on what “mode” you have it in.

For instance on page 3-2 it states the following:


  
  In the Racing Mode, the Saturation, SkinTone, Sharpness, and ASCR functions are not user-configurable.
  In the sRGB, the Saturation, Color Temp., SkinTone, Sharpness, Brightness, Contrast and ASCR functions are not user-configurable.
  


Then on page 3-3 specifically about the Blue Light Filter it states


  When Blue Light Filter is activated,the default settings of Racing Mode will be automatically imported.


Based on what you’re describing, that “blue light filter” may be one of the options that get disabled when selecting a certain mode.