Depending on how much of the ‘look’ is down to it being an analog display device and the assorted tradeoffs of various aperture grills or shadow masks; and how much is down to the historically unavoidable ‘the light is being emitted from behind a curved sheet of fairly thick glass’, the approximation might actually be pretty close indeed.
For the ultimate in authenticity-with-solid-state-convenience, though, you could take an actual CRT display’s front glass and phosphor assembly; remove the electron beam handling stuff and pump the phosphors with UV OLEDs instead.
Markedly thinner, no high vacuum, electron guns, purity issues, etc. but looks a whole lot like the real thing because it’s exactly the same phosphors glowing in exactly the same places behind exactly the same glass. Probably wouldn’t be worth the trouble; but many of the neat things in life can’t really be justified.
