The original Bat character did carry a gun, it wasn't until later the comics retconed and rewrote the character
Yeah, a year or two
later. Sure, 1938 Batman was a gun-toting pulp hero, but that had been abandoned by the early 1940s. The way you say it implies that it was the status quo for a long time, but that's simply untrue. It was an early, tentative portrayal of the character that was swiftly abandoned along with other first-draft elements like the hyphen in his name, the purple gloves, and the New York setting.