I think my question is just going to prove that I don't understand Matter correctly yet but here goes:
I have just purchased an Echo Hub in the UK, and when adding a device to the Echo Hub and selecting Matter, I can select a device type of 'Hub'. There are lots of Hubs listed but not HE. Will HE eventually be one of those listed? And if so, what timescales can we expect?
Hubitat is a Matter controller. This means you can pair devices that support Matter to Hubitat (i.e., bring them in). It is not a Matter bridge, meaning something that creates Matter devices for other Matter controllers from arbitrary devices on your hub (i.e., exposing them out). The latter isn't impossible, but I have seen no indication that it is planned (nor is it what most hubs mean when they speak of Matter support).
I'm not sure I completely understand your question (and a lot to the Matter intricacies) but HE does support matter as a bridge/Controller. You would add your device to your Echo hub, then in HE you need to go to DEVICES>ADD DEVICE>MATTER then get the pairing code for the device from your Alexa hub and connect it to HE that way.
As for timelines, HE Rarely discusses timeline unless something is immediately imminent. Sometimes there are some poorly kept secrets, but as a rule they don't talk about it until there is something definet to talk about.
My hope was to expose Alexa devices to HE, as I already use the Alexa skill the other way. My reason for this is to have all logic rules on one platform (HE) rather than splitting them across Alexa and HE as I do currently.
For that, Alexa would need to be a Matter bridge, and I'd doubt they have plans for that. However, if the devices on Alexa are Matter devices, you can use Alexa to put them in pairing mode and also add them to Hubitat. (Matter supports this kind of configuration, which may be new if you're used to Zigbee and Z-Wave.) This, of course, won't help with other things devices.
It should be noted that if you really want at least some control of such devices in Hubitat -- assuming they can't be directly paired -- you can use workarounds like exposing virtual switches or sensors from Hubitat out to Alexa, plus some automation (Routine) on the Alexa side. But unfortunately, Amazon does not expose an official means of "exporting" these devices, and there isn't anything that can be done in the Hubitat side to change that.