It's definitely not an officially minted halfpenny. It seems actually to be "triple-struck" - I can see the "1773" three times.
Which also lends weight to the conterfeit hypothesis - a counterfeiter would be less careful about quality.
I wouldn't think it to be a "mint sport" deliberately made by the counterfeiter to sell for profit; while collectors of tokens began to appear in the 1790s, nobody was really into collecting errors back then - an error was a "flawed coin" and worth less, not more, than a perfect error-free example.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis