Is there some official or standard specification for an EK20 fitting?
At this point my best understanding is that &quot;EK&quot; doesn't refer just to a pipe thread but more specifically to a specific set of fittings used to mate a tube to a threaded device. The thread standard is just one part of what EK20 means.
Here's an example EK20 fitting, used to attach a PEX tube to a manifold:


The internally threaded female hex collar secures the assembly onto the manifold
The ring is compressed around the tubing (seal #1)
The T-shaped barb accepts the PEX and also mates to the manifold with an O-ring (seal #2)

There are other sizes of the same style of connection, like EK25 (25 mm ~ 1 inch), which appear to work the same way.
I think the benefit of this style of connection is that it allows many different pipe/tubing sizes to be connected to the same device, just by choosing the right EKxx adapter. Its also an efficient 2-for-1 design in the sense that the single threaded ring secures both ends and no special tools are required.

As far as the thread itself goes, I found some product documentation from one supplier which states:

[the product uses] a 20mm Eurokonus (EK20) connection also known as G 3/4&quot;

G 3/4 is a standard British parallel pipe thread size (BSPP). (ref)
This statement is presumably accurate, but isn't as &quot;official&quot; a source as I would like, ideally.
Assuming that EK20 thread = G3/4 that does explain why a US garden hose thread almost fits but doesn't seal. US GHT and G3/4 are only similar:

The GHT and BSP standards are not compatible, and attempting to
connect a GHT hose to a BSP fitting, or vice versa, will damage the
threads.

(https://en.wikipedia.org/wiki/Garden_hose#Standards_and_connectors)  Wikipedia also notes that the GHT is 3/4 diameter but 11.5 threads per inch, whereas G3/4 is the same diameter but 14 threads per inch. So the GHT female would screw on partway but then bind up and probably not make a tight seal.

A remaining unknown  -- The inner O-ring I assume must have standard dimensions, given that it makes an internal seal in the EK20 male portion. But I don't yet have any information on what this standard might be. Without this detail it would be hard to know if a standard (BSPP) part would effectively seal to it or not. However, I do have some proper EK20 caps that use an external O-ring to seal (just like in a garden hose), which work fine.