Alright - I have a working theory.
I pulled the Tweet using the API, and it shows up with a scopes attribute. These are used when the Tweet has been targeted using the Ads platform. Based on the associated place ID, it looks like this is scoped for geotargeting to the UK.
I’m guessing a bit here, but a) I’m not sure promoted / scoped Tweets are supported in widgets and/or b) perhaps the server where the site hosting the widget is running isn’t seen as being in the geo region, for some reason.
I’m still slightly surprised that I can’t see the Tweet in your timeline since I’m located in the UK… I’ll see what else I can learn about this, but I’ll need to chat to the Ads team about it.