The invisible hand disappears
That's something of a distortion. The phrase occurs exactly once in Smith's most invoked work, The Weath of Nations. It appears in Book IV, Chapter II:
Of Restraints upon the Importation from Foreign Countries of such Goods as can be Produced at Home, in the specific context of merchants choosing domestic products over imports:
By preferring the support of domestic to that of foreign industry, he intends only his own security; and by directing that industry in such a manner as its produce may be of the greatest value, he intends only his own gain, and he is in this, as in many other cases, led by an invisible hand to promote an end which was no part of his intention.
This is hardly a major part of the text. Many editions, including the Pelican Classics edition on my own shelf, omit it entirely. And it's highly questionable whether such buy-British behaviour is now a significant phenomenon, if ever it was.
The phrase also occurs once in Smith's other key work, The Theory of Moral Sentiments, in a passage proposing that wealth naturally spreads from a few rich to the mass of poor:
The rich only select from the heap what is most precious and agreeable. They consume little more than the poor, and in spite of their natural selfishness and rapacity, though they mean only their own conveniency, though the sole end which they propose from the labours of all the thousands whom they employ, be the gratification of their own vain and insatiable desires, they divide with the poor the produce of all their improvements. They are led by an invisible hand to make nearly the same distribution of the necessaries of life, which would have been made, had the earth been divided into equal portions among all its inhabitants, and thus without intending it, without knowing it, advance the interest of the society, and afford means to the multiplication of the species.
More recent economic and demographic work on income distributions tends not to support this charming proposition.
The vast majority of Smith's writings runs counter to the instincts of many of his loudest invokers, as set out at length in Iain McLean's recent Adam Smith, Radical and Egalitarian. Personally, I've found that anyone invoking Adam Smith and his Invisible Hand almost certainly doesn't really know what the hell they're talking about.