Star Trek: Deep Space Nine and Star Trek: Prodigy don't have a lot in common. Deep Space Nine was a live-action show, filmed in the 1990s, and was set on a space station. Prodigy is a show from the 2020s, animated and follows around a group of young aliens as they try to make it in Starfleet, all while being instructed by the legendary Kathryne Janeway.
They are both fantastic episodes but beyond being Trek, neither show has a lot in common. That is, until now. The season one Prodigy episode, "All the World's a Stage" saw the crew of youngsters land on a planet that has taken to living their lives through the Starfleet mantra. They even dress up in similar Starfleet-inspired uniforms, as they believe themselves as part of Starfleet.
Apparently, though, this was a story that was going to happen in Deep Space Nine. According to a DS9 DVD special feature (and CBR), it's been revealed that the original premise for the episode would be Trials and Tribble-ations was actually meant to be a bit different. The show would actually go back to the original series episode "A Piece of the Action."
Ronald D. Moore and Rene Echevarria wanted to do a different story, one that saw the crew of Deep Space Nine return to Sigma Iotia II, the home of the 1920s-era Chicago cosplaying aliens. This time, however, according to the article, the DS9 crew would return to find that the entire now resembles Starfleet and that the inhabitants all were dressed up as the 1960s-era Star Trek series.
This of course was to be a salute to the then-30 years of Star Trek, an idea that Trials and Tribble-ations would do much better. In fact, not only was the end result far more sincere and lovely than what was presented, but Prodigy did a much better job with the same idea than Deep Space Nine would've done. The original concept would be treated very tongue-in-cheek-like, and not at all as sincere as Prodigy played it.
"All the World's a Stage" remains one of Prodigy's best episodes to date.