I think that most people mean "foreign" as foreign government (such as CCP) support, not just support from middle-class Americans (and Europeans) who identify with the protests and happen to be foreigners.
And while it could be that foreign governments have donated with false identities over GSG, it is more likely that they would send in people to figure out who is really capable of moving things, and contact them with cash, tips, and resources.
(I am not commenting on the envoy, as so far have only seen it in news outlets [such as CNN & NYT on the left and Fox on the right] who have not earned my trust - so I do not know what is really happening.)
As a Canadian I absolutely count donations from foreigners in the US and Europe as foreign money and absolutely think that that should be illegal (though I have no clue as to what the current legal status of that is).