I would bolt a piece of angle iron to the existing metal frame. Set one face flat against the metal frame and the other flush with the bottom of the current top, and extending out far enough to support the new top. Put a few screws into the new top to secure it in place.
I recently added a desk extension so I had the same problem, I needed the two surfaces to be flush and stable. The solution I came up with was to use a dowel jig to drill dowel holes at the same depth below the level of the top surface, then used dowels to join the surfaces, which worked very well and I'm pleased with the result.
Once you have the two ...
I think this is all you need to do after getting a wall mount monitor.
Build wood frames with studs enclose the monitor (similar to building a window frame), place plywood backboard, and attach the monitor to the board using the mounting hardware shown. Now everything will be hidden behind, and you don't need to worry about overturning since the offset is ...
If the backboard's only purpose is to mount monitors, there are other solutions. I have Adjustable Gas Spring Monitor Arms that you can clamp to the back of the desk, or even put a mounting hole in the back of the desk instead of clamping. The one I use supports 2 monitors and extends up to 24" from the mount (ends up about 18" from the back with ...
The structural question is: what will provide support for the moment-force of the monitors hanging off the backboard?
You can provide torque support for upper back-panel, by means of
side panels as in "yesteryear's" computer desk (see other answer), or
lumber behind the back-panel, as you propose
Lumber "on edge"
To provide the most ...
Your plan should work quite well assuming you do not mount your monitors too high and make it all top-heavy. I also assume this will be pushed up against a wall so that it cannot easily fall backwards either.
Your design is a much sturdier version of the common computer desk with hutch of yesteryear.