okrish

As black glazes become more matte they become more grey/metallic. A glossy black can be very black despite it being glossy, and will be blacker than a matte black. As others have noted, you're not going to find a glaze that has the non-reflective quality of the Black 4.0 simply because that's not how glazes work. It can only be so matte and still melt. A black underglaze can be quite black and non-reflective, but it's not going to be food safe because it doesn't go into melt like a glaze. If food safety was not an issue you could go that route, or possibly even use black stain in a porcelain clay body.

1. Far more detail on carbon-nanotube based  black paints than any of us can handle.
https://www.paint.org/wp-content/uploads/2021/09/Carbon-Nanotube-based-Black-Coatings_Mar-2021.pdf
I think it clearly indicates that this class of material is in a different league from anything you will be able to achieve with a glassy glaze.
2. Although it won't be very robust, it might be fun to glaze a teacup with a black glaze and then  paint the outside with Black 4.0.
- there are several options for handling the outside of the cup
-- leave unglazed then paint with 4.0 (maybe over an acrylic undercoat)
-- paint the 4.0 on top of the glaze (maybe over an acrylic undercoat, perhaps one sold for acrylic-on-glass work)
-- maybe leave a lip-ring of untreated glaze (H&S, wear, etc)
- Looking at how stained my tea mug gets (and how difficult it is to clean) I don't think it's sensible to try and paint the inside of the cup.

3. In some ways Black 4.0 is reminding me of day-glow colours. Both are, I suggest, so dramatically eye-catching because the human visual system has difficulty assessing the reflectance of the surfaces (almost zero for 4.0 and "greater than 1" for day-glow colours). The day-glow phosphors convert UV light to a narrow visible band, so more light is emitted  by the object in that waveband than hits it.

Firstly, I don't doubt Bill's advice that a clear glaze over a black glaze may make it appear blacker.
However IMHO it emphasizes the real differences in the physics of Black 4.0 and glazes (pedantically the surface of the Black 4.0 pigment and the surface of glasses/glazes). Because covering Black 4.0 with a varnish seems to loose the magic †.
Black 4.0 claims to reflect about 0.05% of the incident light (this varies with the incidence angle of the light ‡). For window glass (and presumably glazes, which are glasses) the figure is a lot bigger (even with an anti-reactant coating).

 
† https://help.culturehustle.com/en-US/articles/black-40-faqs-121873
No, sadly this paint is not waterproof and may get damaged outdoors. There is no clear varnish as matte as this paint to protect it and attempting to use any top coat over BLACK 4.0 will likely ruin the finish.
‡ https://www.dpreview.com/forums/thread/4739693
Black 4.0 - deeper into the Dark Side?
PS If pressed I'd be inclined to try these options.
1) A clear base glaze containing lots of black stain. Maybe looking at the difference in appearance a matte base-glaze gives.
2) A deeply matte copper oxide surface (based on a copper matte raku but without the color-forming reduction). Wildly non-functional, but the optics might be interesting. I haven't tried it but Hasselle Copper Matte is  a frit/glass less copper matte recipe in
https://ceramicartsnetwork.org/docs/default-source/uploadedfiles/wp-content/uploads/2015/08/15rakuglazes.pdf

In case someone reading the thread becomes so intrigued with Black 4.0 they simply must order it, I feel obliged to make a little public service announcement. I ordered some about two and a half months ago (May 7). It’s not here yet. I waited till the two month mark to email them and got an auto generated response apologizing for the wait and informing me that I was near the “top of the queue.” Poking around the web a bit I see this is a common experience. So, be prepared to wait, I guess.