This is possible with coloring and Extrude & Bevel. You extrude the edges and what's outside the hole and add something at the bottom.

It's actually a layered structure:

The text and frame. It's here blue, but it must be nearly or full white when extruded
The result of the extrusion. It has plastic shading. There's low ambient light to get contrast
Top layer has a gradient with blending mode Hard Light to give some apparent form
Bottom layer has another gradient to make an illusion of metal
If you need roundings in 3D it can be achieved with expanding the extruded shape and applying gaussian blur. But to prevent the result be unsharp, make a copy of the non-blurred shape, unite in the pathfinder panel all subshapes, color to white and use it as transparency mask to remove all blur outside the apparent piece:
The difficulty increases radically if you want to simulate insets to a strongly curved surface. I would leave it to 3D programs. Low curvatures probably can be handled with envelope distortion. An example of 3D:

This is a 3D wireframe and a screenshot of a shaded view of letter A imprinted to an oval knob. Unfortunately the shaded image is a screen resolution bitmap only, it can have only one color and there's no materials (typical limitations of easy to use freeware). But the wireframe can be taken to Illustrator (in this case only as PDF print) and colored there. If you succeed to imprint your shapes into the curved surface as 3D and get the wireframe scene (hidden lines removed) to Illustrator as vector, it surely reduces the drawing effort at least 50% when compared to drawing it from scratch.
ADD due the comments: The used 3D software is DesignSpark Mechanical, it's freeware. Altough it's very good in some cases, just this example needs some fighting. It has no text tools, the A is a drawing. It's so small that the curvature of the surface caused no problems. A is itself curved. Texts with real fonts can be made with trickery by retyping numerical dimension labels. It's difficult to place things exactly because there's no snaps, you must work with high zoom and carefully remember the placements and positions of the parts. But it's possible to project as well texts and numbers and drawings onto a curved surface. Here's a screenshot of one such battle result:

Making insets for single numbers and letters or other small simple shapes has a serious difficulty: The shading ambiquity. The result seems to be an extrusion as soon as the bottom is totally visible. The viewing angle should be low enough to hide a part of the bottom behind the edge. It can be seen also in your gearstick image. There's no exact limit how much of the bottom should be hidden. The problem has been discussed here Adobe Illustrator: Making a shape appear to be "carved" into a surface
I crunched together an example with text:

The extruded plate as flat and colored to blue. The extruded version was white
The extrusion result. It's quite grey due low ambient light and low light altitude. There's no bevel. White background doesn't fit if one wants insets instead of holes. The viewing is from too high, at least my eyes see it at first as a hole and then it's something above the plate.
A grey backplate has been inserted and the extrusion has got a bevel. The backplate fixes the holes. The bevel seems to reduce inset-outset ambiquity.
The gradient which is used in 5 and 6
An attempt to transform it to metal: The extruded shape has got Object > Expand Appearance which fixes the 3D effect. All parts are selected and a gradient color fill + a thin grey stroke are inserted. There's also backplate with that gradient
The backplate separately. It's made by unifying all shapes of the expanded extrusion with Pathfinder panel's unite. Then the compond path was released to separate the hole shapes. All was filled with the gradient (releasing made a group, the gradient was inherited from the compound path to all parts)