Not sure I have ever seen a company use a .eu domain - which I suspect was set up as a vanity project by the eu.
They confuse people, .com, people can deal with, .co.uk people can deal with, but older and non-technical people can struggle with what is out of the norm (although not new).
These people, unlike us techies aren't visiting .io domains or .xyx domains.
When I've tried to use .uk sufficient people have understood it to mean .co.uk that is was a problem.