Track hardware for hanging plywood panels

"Sliding rail" and "rail hooks" are the search terms you are looking for. See places like McMaster-Carr sliding tracks, at least as a start.

If this does not suffice, as it looks like your reference design is custom, you can consider modifying the common t-slot designs used in many commercial applications. We've all seen the "wall of slotted engineered veneer" at stores with matching installations that hook and slide on with keyed sliders.

The rail could be a robust plywood with one or more slots in it (so you could adjust for height, as well!) and the runners would key in similarly within insets.

Maybe not the turnkey solution you are looking for, but that may only be available in B2B markets. You may have to trade off making your own solution now for some perfect solution you hope to find in the future.

Amazon and places like Lee Valley offer examples and (usually router) tooling to make your own.

To recap:

1. You might find the exact hardware with more internet sleuthing, though it appears you've exhausted most avenues, leaving you with the long tail of searching B2B manufacturers.
2. French cleats. Not perfect for your application, as the inset and top rail might get a bit large. But very cheap, and easily made in the home shop. Metal cleats purchased from any online shop could be very low-profile.
3. T-Slot (or whatever letter is appropriate) design similar to a French cleat that would be a little more complicated to make, but could be made a little lower profile that traditional French cleats.

Note: I know that some folks refer to the latter two both as "French cleats" But I'm making a distinction here. There is what I think is the traditional cleat, made from convenient lumber (or metal) as a pair of simple mating surfaces. The slotted design is more of a commercial system that usually requires a router with some special tooling, and specific keyed runners. But you may run into places that conflate the two. (I don't care who's definition is correct -- I'm making a distinction for the purpose of answering the question "how can I solve my problem in a similar manner as the described hardware".)

It also depends if you require the unit to move smoothly, as if on bearings or wheeled tracks. If so, none of this advice will do, and you will need to shop for a solution, or engineer up a very interesting solution.