Brilliant!! You definitely seem to have some uncanny intuition for these things.
When the Story is in full screen, right click does nothing - so is disabled. Left click prematurely ends the video (* see caveat further down).
But here's the weird unexpected part (again, I would never have looked for this if you didn't ask):
Firstly, when the Story launches in full screen, there is a play button if the story is a video, not a picture. There is also on the top left of the screen a progress bar that runs to completion, whether you play the videos or not (in this mobile mode the videos don't seem to play automatically), after which the Story exits full screen. Stories can consist of multiple segments with videos and/or pictures. The mentioned progress bar is broken into segments if multiple parts, but it runs through all of them.
After going back to the normal Instagram screen (the second part of your question) VDH is not lit up. Big disappointment!! But when I open VDH, there is a grey 'Orphan' dot with hits. The number of hits is the number of video segments that the Story has. Note, pictures are excluded (VDH only downloads videos). Also, if you exit the full screen before it has run through all the segments, only those videos encountered appears in the hit list.
Next thing to remember: Orphan hits in VDH disappear after a set time. Default is 60 seconds, but it can be changed in Settings. So, download while you can - otherwise you have to do the process again.
Stories often consist of only one segment, but can also contain many segments. (In Instagram they also have a Saved Stories feature, where the user can keep Stories permanently.) This is shown in the progress bar having multiple segments. You can leave it to happily run through all the segments. Videos won't actually play, unless you press the play button - but you don't have to play them (and it's faster not to play them). VDH still detects them as a hit. You can make the progress bar move quicker through the segments by left clicking anywhere on the screen. (Yes, I know I said that left clicking exits the Story, but that's only on the last Story, or if there is only one segment.) *
As we all know, nothing is ever simple and predictable. When you speed up going through multiple segments by left clicking, afterwards VDH actually has some proper hits (it is lit up) and some sitting in orphans. I think it might have something to do with whether a particular video segment had enough time to actually appear as an image (they sometimes take a second or two to load) or not. It seems random (probably isn't) but I won't investigate that further. I think if you leave the progress bar to go at its own pace, or when you click to speed it up, at least wait for each image to appear, they will all go into orphans. At least they are all together then.
I used the Shift key while selecting the downloads to prevent VDH from closing the drop down screen. I find it better to start at the bottom, as these are short videos and very quickly reappear as a downloaded video but with a play button, which you can accidentally launch. Here it would be very useful to have a VDH function to select 'Download all videos'. I think the feature has been asked for before.
Conclusion: In my earlier method, you can skip creating a fresh Firefox profile (unless you want a permanent profile set as Mobile user agent). Just install the User-Agent Switcher add-on in Firefox, select Android / Firefox 83 mode when you need to download a Story video, and run the Story. Afterwards, check VDH for the grey orphan hits and download the videos there. Afterwards you can switch the user agent back to default mode.
Thanks again, Mjs!! It was a very fruitful collaboration. (By the way, I am a retired electrical engineer and programmer - so used to fiddling with things, though I don't always have the enthusiasm and energy for it anymore!)
Pierre