[Retrofitted]

As you found out, mostly it's down to Hollywood and gang culture, so I went after the Hollywood angle because I remember seeing it in some gun-fu movies in the 80s. So...

ChatGPT's response:

The exact first movie to show the sideways pistol grip is difficult to pinpoint, but one of the earliest and most influential films to popularize this grip was John Woo's "A Better Tomorrow" (1986). This Hong Kong action film featured stylized gunplay and introduced the concept of "gun-fu," where characters often held guns sideways during shootouts. The film's influence, especially on action cinema, helped spread the use of the sideways grip in other movies.

However, in American cinema, the sideways grip became widely recognized in the 1990s, particularly in films depicting urban gang life. "Menace II Society" (1993) and "Boyz n the Hood" (1991) are notable examples that brought this grip into the mainstream, associating it with gang culture and street violence.

These films were instrumental in embedding the sideways grip into popular culture, where it became synonymous with a certain "tough guy" image, even though it was more a stylistic choice than a practical one."

[Jonty30]

Chatty lied to you.
https://truewestmagazine.com/article/the-sideways-grip-cool-or-crazy/

[Jonty30]

Here are other movies.
The fact that it came out in the 1960’s would suggest some military connection, since many of the actors of this time period did serve in WWII and the Korean war.

https://www.pagunblog.com/2009/12/15/origins-of-the-sideways-grip/