The use of IMAX 70mm would not have had any measurable effect on the narrative or storytelling. In fact Christopher Nolan acknowledged in several interviews surrounding the film's release that the vast majority of filmgoers would not see Oppenheimer in IMAX 70mm (which is different than the more common digital IMAX). While he recommended this as the best experience, he gave no indication that someone would miss anything of narrative substance by seeing the film in a more conventional format.
Movie technology such as widescreen, anamorphic widescreen, multi-channel sound, and large film formats serve a primary purpose of creating immersion, i.e. drawing the audience into the dialogue and action. In many ways these technologies work best when the audience doesn't notice them, similar to a film score where the goal is to enhance the experience, not distract from it.
Widescreen accomplishes this because our brains focus our visual attention on what is in front of us and to the sides, so a widescreen presentation fills this space in a way that causes the theater to somewhat disappear. IMAX can do this to an even greater extent. Although the IMAX 70mm aspect ratio is more narrow than widescreen, IMAX 70mm theaters display the image on the full width of the screen, as well as almost literally to the floor and ceiling, so that basically all you see is the image. And without any (or much) distracting graininess. In a New York Times article (the article is behind a paywall) about the use of IMAX in the more intimate scenes in Oppenheimer, Nolan is quoted as saying:
“The screen disappears,” Nolan said. “So you’re in intimate space with the subjects.”
An interesting secondary reason given by Nolan in the article is that when a film is essentially "dressed in a tuxedo" (my words) it can create more buzz and interest about it even for those who don't see the movie in that format. In Nolan's words,
“The event, epic size, quality of that trickles down to the excitement for the film in all other mediums, down to when somebody’s watching on their telephone,” Nolan said. “They have different expectations of what a film that has been distributed in that way is. And so it’s always been important beyond the sheer number of screens.”
This is important since only thirty theaters worldwide showed Oppenheimer in IMAX 70mm, and a slightly smaller number of IMAX GT dual-laser theaters. These are the only theaters where the full immersion of IMAX can be experienced.
Shooting films with IMAX is expensive and time consuming, which is why only a portion of Nolan's (and other director's) films are shot in IMAX. For example in Star Wars: The Force Awakens (2015) only a six-minute action sequence was shot in IMAX. In the case of Nolan's films, The Dark Knight (2008) was about 20% IMAX, The Dark Knight Rises (2012) about 40%, Interstellar (2014) about 40%, Dunkirk (2017) 70%, Tenet (2020) 50%, and Oppenheimer (2023) about 25% (all based on various online commenters not official sources). In most of Nolan's IMAX films the remainder was shot using regular 70mm film.*
*both 70mm and IMAX 70mm are actually shot using 65mm film stock and printed onto 70mm film for theatrical release.