Not sure why you're accusing me of lying.
I am not accusing you of lying.
I am making the point that 'reach out' is still a modern day Americanism regardless of any tenuous evidence of it being used in 6th century Old Norse, or anything else. Unless of course Americans have been using it for centuries too, which it appears they haven't - or no-one would be going to the bother of writing whole articles on its sudden wide emergence as an idiomatic expression.
Whether or not it is a 'total neologism' seems beside the point. If no-one in living memory can say they ever heard the idiom being used regularly in the English language (American or otherwise) until a handful of years ago and that when they heard it it was from the lips of Americans or through the writing of Americans then that is new enough and American enough for most people.
Whether certain features of American English are rooted in archaic English (much like Canadians with French as a first language speak a version that is rooted in archaic French) is also beside the point.
I am certainly not arguing that British English is 'right' and American English is 'wrong.' But the fact is that we in the UK haven't been using certain archaic words (for example the recently ubiquitous 'gotten') for centuries and if we are starting to use them again now, it's not because of Shakespeare or Chaucer or Old Norse or the modern day Icelandic descendents of Norsemen, or anybody else - it's because of Americans. Now. In this century.
As much as the contextual history you add is fascinating, to insist that the influence of contemporary American culture is not the reason these affectations are are seeping into British English now just comes across as needlessly pedantic and nit-picky.