Map an image file to a UV dome post-version 2.8 Version 2.92.
Created a UV sphere and lopped off half, so a hemisphere remains.
At present there are by default two panes in the UV Editing tab screen--UV Editor and 3D Viewport, side by side.
After Edit Mode!UV!Unwrap in the right pane (in the 3D Viewport), the UV Editor (left pane) changes from a square grid and a cursor in the lower left, into a round grid that can accept a round map--where I've thus done so:

Meanwhile the 3D Viewport (right pane) contains the dome perspective, but it's still gray.
I want to map the .png in the left pane onto this dome in the right pane.  But how?
UPDATE:
Here is something in the &quot;Base Color&quot; field for Material Properties:
I have seen the pic you have provided and it is pretty clear that you haven't set the material to Image texture. Please change it to image texture and then try UV mapping it, then it should work.