Did you end up finding something? We are on the same boat and looking for options.

Task Lighting sold by primary distributor Hardware Resources as well as several other sources on the internet has the lowest-profile outlet strips I've seen anywhere, the APT series. They also have units that are outlets and lights combined for under the cabinet, but i am not sure if they offer those in the low-profile option as well. You can check out the brand here: https://www.hardwareresources.com/tasklighting

The Legrand Adorne system also has a nice-looking under-cabinet lighting system where the lights themselves would fit into your space although the outlets wouldn't be as low-profile. You might want to take a look and see if you like the look of Legrand Adorne and could live with it even if it is a little bulker than you wanted.

I found the Adorne and unfortunately it was bulky. I looked at the Ikea Utrusta but I also saw it was no longer sold in US or Canada.

I'll check out your link, thank you! I wonder where this developer got the shelf its sleek and trim and flush but no luck at all yet. Hopefully someone knows another option as well.

Many types of slim-profile lights are available, but if you want an outlet strip as well, I haven't seen anything smaller than the APT series by Task Lighting. You may need to find another website to get the actual specs, but the height should be 1 1/2" and depth 1 1/16" with powder-coated finish in several color choices. You can also get these with lights attached. They can be custom-made to your length and outlet specifications. Unfortunately, when it comes to outlets, there is a limit to how small they can be.