Warning: SPOILERS for Star Trek: Prodigy Episode 3 - "Starstruck".
Hologram Janeway (Kate Mulgrew) showed the USS Discovery in Star Trek: Prodigy episode 3's history lesson but here's why this doesn't break canon. Janeway surprised the young rebels who stole the USS Protostar at the end of Star Trek: Prodigy's series premiere. In Star Trek: Prodigy episode 3, Hologram Janeway gave Dal R' Rel (Brett Gray), Gwyn (Ella Purnell), Rok-Tahk (Rylee Alazraqui), Jankom Pog (Jason Mantzoukas), Zero (Angus Imrie), and Murf (Dee Bradley Baker) their first lesson in the history of Starfleet and the United Federation of Planets, which surprisingly included a starship resembling the USS Discovery.
Some Star Trek fans who are obsessed with canon cried foul when Hologram Janeway included a Crossfield-class starship identical to Star Trek: Discovery's eponymous vessel in her history lesson, which included other famous ships resembling the USS Enterprise, the USS Defiant from Star Trek: Deep Space Nine, and Janeway's own USS Voyager. The issue with the Discovery being grouped with this fleet of starships is that the Federation isn't supposed to know what really happened to the Discovery until Burnham and her crew rejoined Starfleet in the 32nd century. Michael Burnham (Sonequa Martin-Green) and her ship were wiped from Starfleet records by Spock (Ethan Peck) at the end of Star Trek: Discovery season 2 after they time-traveled to the year 3188 in a one-way trip.
However, assuming the Crossfield-class ship Hologram Janeway showed Star Trek: Prodigy's crew actually is the USS Discovery, this actually enhances Star Trek canon instead of breaking it. What Spock did at the end of Star Trek: Discovery season 2 was falsify Starfleet records to say that the USS Discovery was destroyed with all hands lost during the battle against Control. Spock also deleted all records of Discovery's spore displacement hub drive and both steps were necessary to prevent anyone (including Control if it was rebuilt) from being able to use the spore drive to destroy the galaxy. However, Spock didn't change the fact that the USS Discovery and Michael Burnham, existed so both are a matter of Starfleet record in the 24th century (and it would be 800 years until Starfleet learned the truth about what really happened with Burnham and the Discovery).
Meanwhile, the USS Discovery wasn't the only Crossfield-class starship built by Starfleet. In Star Trek: Discovery season 1, the Discovery had an identical twin science vessel, the USS Glenn, that was also working on perfecting its own spore drive before a freak accident destroyed the Glenn. While it's possible the Glenn and the Discovery were the only two Crossfield-class ships operating in the mid-2250s, there was likely a USS Crossfield as well that was the original prototype for that class of starships.
Of course, a logical real-world rationale for why what appears to be the USS Discovery was part of Hologram Janeway's history lesson is that Star Trek: Discovery is the flagship of Paramount+'s growing fleet of Star Trek series. It's merely smart cross-promotion to include the USS Discovery, which is now one of the most important ships in Star Trek along with the Enterprise, the Defiant, and Voyager. Further, Star Trek: Discovery season 4 will stream concurrently with Star Trek: Prodigy on Paramount+ starting in mid-November so it's smart to incorporate the newest Star Trek series with the show that started the current generation of Star Trek shows on-screen.
Within the context of Star Trek: Prodigy, Hologram Janeway knew she was speaking to a young crew who she interpreted as Starfleet cadets. It makes sense that Hologram Janeway would choose a Crossfield-class ship to join the other starships she showed Dal, Gwyn, and the others because the USS Discovery is simply a cool-looking ship. If Hologram Janeway wanted to dazzle Star Trek: Prodigy's young cast with some of the best-designed ships in Starfleet, she certainly accomplished her mission. Evoking the Discovery along with the Enterprise, the Defiant, and Voyager also reminds fans that Star Trek: Prodigy is officially a part of Star Trek canon.
Star Trek: Prodigy streams Thursdays on Paramount+.