A simple subdivide and hook was used here -
The front surface of a cube was inset to provide outer panels and the screen area.
The screen area was subdivided 64 x 24 (32 x 24 would probably do)
A "Graduated" hook (see below) was added to pull those vertices out from the case, concave fashion .
With the curve right, the Hook Modifier was 'Applied' to give us hard mesh with the still bulging screen.
The screen's vertices were again selected and pushed back to be inside the case.
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Graduated Hook -
...is an ordinary Hook with it's "Radius" slider set to non-zero. The value 0.7 was used here and the Hook placed a little in front of the subdivided screen.
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EDIT - 7th Oct 2022
Should the case's front need to be curved also...
Make the case first. Add a cube and subdivide it's front face 32 x 32.
Use a Graduated Hook to curve it.
'Apply' the hook modifier so you end up with hard mesh.
Now armed with a curved case, an aperture can be 'punched' out with an impaling cube using (by preference) the 'Knife Intersect' tool. (CTL-F --> Knife Intersect)
With the hole in place, extrude it's borders back into the case and scale those vertices down a little.
Those vertices will give you your screen size so duplicate those in Edit mode and part them.
There'll be heaps of intermediate vertices along the edges and they're going to be a real nuisance so dissolve all but the outer 4 corner vertices. You just want a rectangle with 4 vertices.
With the unwanted vertices gone the screen rectangle can be subdivided 24 x 24? and those vertices curved with a hook to match the case's curve.
Expand the result slightly so it penetrates the case's extruded sides and avoid gaps.
It can remain a separate object, parented to the case, or joined to it.