As you say, we've been working on solid adsorption for a long time now. Nothing has left the lab. The video presents an optimistic future, but we don't even have the basics yet.
Firstly, there is a fundamental issue - H² doesn't really give you anything to work with. The vast majority of compounds have two protons, two neutrons (rare isotopes have more protons). [They're distributed in the most boring orbitals, just spheres with no real edge to gain leverage.](https://winter.group.shef.ac.uk/orbitron/atomic_orbitals/1s/...)
This lack of leverage makes surface adsorption tricky. The molecule gives us nothing to grab. You won't carefully craft a surface that can hold H².
I think right now there's a focus on activated carbon. That's become a bit of a synonym for 'graphene', with it's well known limitations.
When I studied the subject, metal-organic complexes were the focus. These would be extremely customisable, but if they worked we'd probably have seen by now. They tended to use heavy metals. I wasn't optimistic at the time, I thought anything using materials past the 4th row of the periodic table was unrealistic. As the metals get heavier they get expensive and sometimes rare. If we want to solve a common problem, we need common components. If your solution has lanthanoid, it won't scale.
I was right btw. The research group closed when funding was reallocated. Each experiment ran the research budget of another group. MoC's don't really get much love any more.
Anyway, we should probably think about what makes a good hydrogen adsorption material. I think it's pretty simple, you want a material that: stores a high density of hydrogen, is reusable, quickly picks up hydrogen, and quickly releases hydrogen.
The latter 2 categories is the 'kinetics'. Of the materials we know, all (literally all) that have 'good' kinetics are either single use or low density. Conversely, all that are both multi use and relatively high density have poor kinetics. Additionally, most of those with good kinetics have unrealistic conditions, like requiring 400˚C temperature to release the hydrogen.