I have these settings:
Then I get this:
To get rid of the gray parts, I recalculated normals for the cup but the result is the same.
So I tried:
I know the color is transparent, but it's not see through in both ways.
Turn the roughness and IOR down. Eevee is a bit intense with distorting the IOR. Keep opaque settings.
To remove the grey edges turn the 'Edge Fading' to 0.
To avoid any artifacts (if that's what's bothering you), disable the Show Backface option. You won't see any thickness though, for glass in Eevee does have limitations: