Considering how hard the Marvel Cinematic Universe and, by extension, Sony's Spider-Man portion are pushing the multiverse narrative, people probably shouldn't be overthinking how Deadpool will eventually factor in. Deadpool 3 writer Rhett Reese, who's worked with writing partner Paul Wernick on the previous two films, the Zombieland franchise, and more, offered some breadcrumbs to the BroBible's Post-Credit Podcast (via The Direct) on what more we can expect the Ryan Reynolds– starred franchise.
"It's a wonderful opportunity for fish-out-of-water. Deadpool is a lunatic at the center of a movie," Reese said. "To drop a lunatic into a very sane world, it's straight butter. It's going to be really fun." As far as previous explanations on how heroes can randomly pop in, Sony used Tom Hardy's Eddie Brock/Venom to bookend post-credit scenes of Venom: Let There Be Carnage (2021) and Spider-Man: No Way Home (2021). While the actor factored zero into the plot, the post-credit scene in the latter film allowed Venom to leave a piece of itself to exist in the MCU where it could infect that's universe's Peter Parker (Tom Holland). The 2022 follow-up in Morbius randomly dropped Michael Keaton's Adrian Toombs/Vulture (previously in 2017's Spider-Man: Homecoming) to interact with Jared Leto'sMichael Morbius in the post-credit scene.
Doctor Strange in the Multiverse of Madness saw the first official MCU introduction of mutants with Patrick Stewart's return as Professor Charles Xavier in Earth-838 as part of the Illuminati. So what could make Deadpool appear in the MCU? There was the matter of the time machine from Cable (Josh Brolin) that was fixed by Negasonic Teenage Warhead (Brianna Hildebrand) and Yukio (Shioli Kutsuna), which the Merc with the Mouth gloriously abused during the Deadpool 2 prior to the credits. One use too many could send him to Earth-616. The point is there doesn't really need to be an elaborate explanation to see him transported randomly elsewhere to co-exist with the Avengers.