Maybe a real secure kernel, such as SeL4 or LynxOS.

The tipoff that it's not L4 is that it's a desktop OS that runs applications.

You can do a desktop on a microkernel that runs Linux in user-mode or with hypervisor support. Critical stuff stays outside directly on microkernel. It's what every vendor of separation kernels does. Two examples from commercial and FOSS that's similarly alpha:

Sirrix TrustedDesktop on Turaya:

https://www.sirrix.com/content/pages/trusteddesktop_en.htm

Turaya's architecture:

http://www.perseus-os.org/content/pages/Overview.htm

FOSS alternative that they already use to develop itself:

https://genode.org/

Have you use any of those commercial offerings? I've honestly never heard of them before. Can i, as a regular consumer go purchase one of those operating systems and use it on my laptop?

You can go and use Genode right now. There's no installer (to my knowledge) -- you'll have to build the OS by hand. If the area of secure OSes or capability-based OSes are interesting to you, Genode is the best playground for that. The DROPS/Dresden folks have been working in this area for a long time.

Genode is largely kernel agnostic, being an "Operating System Framework" -- you can run it on Linux, variants of L4, seL4, Muen, and more.

You probably have to buy hardware from them if the drivers are on the microkernels because I doubt they're doing many ports. I haven't used the product as I had custom stuff. Here's a video of the academic prototypes that both the commercial stuff and Genode drew from if you're wondering about performance. That's on a Core Duo 2 @ 1.6GHz. The L4Linux VM's were fast.

https://www.youtube.com/watch?v=x9IwtY9gqCg