Did he invent that style or was it en vogue before him and he just popularized it?
It actually came from WW1 when prior moustache styles couldn’t be worn under gas masks.
It had been in American fashion since the late 19th century (it gained popularity for its neat, uniform, standardized style).
Also, Chaplin adopted the (faux) mustache for his Tramp character in 1914, mere months before the war and over a year before the deadly poison gas attacks.
Hitler had a mustache as early as at least WW1 but he had the handlebar syle at that time. Hitler changed to the toothbrush style mustache when he entered politics as an attempt to become more popular because in Germany in the 20’s Charlie Chaplin was one of the most famous and beloved people so Hitler attempted to copy Chaplin to gain more support
Wasn’t it already well-known before Chaplin? It was an American import at the end of the 19th century and it was pretty popular even then. Chaplin just made it funny.
It was a known style, Chaplin is just the direct reason Hitler chose that style