Star Trek has returned to epic crossover stories, a stable of the 90s. You couldn't go a season without seeing someone, from another show, popping up in another series. Jean-Luc Picard cameoed in Deep Space Nine's pilot, as did Quark for Voyager's. We saw William Riker (or his clone) in nearly every show he could find time to appear in. Q was everywhere but in very limited quantities.
It was a fun time to be a fan. Yet, as the Nu Trek Era began, crossovers became a thing of the past. Sure, Seven of Nine was a major player in Star Trek: Picard but she wasn't seen as a cameo or guest star, she was part of the main cast. So she didn't really feel like a 'crossover' character.
Star Trek: Lower Decks would start doing cameos, a trend we'd see go into Star Trek: Prodigy, but as neither show was actively taking characters from other active shows, it's fair to say that they don't really qualify as crossovers.
So we're left with two episodes; "Those Old Scientists" from Strange New Worlds and "Fissure Quest" from Lower Decks. Now, I would consider a crossover to be a show that only takes characters from other series that are actively on the air in some form or facet. So I don't think Fissuree Quest counts, but the fandom seems to believe it does. So for that reason and that reason alone, I'll treat "Fissure Quest" as a 'crossover' episode, even though it's more of the same from Lower Decks; just with more cameos than ever before.
Of these two episodes, some believe that Lower Deck's attempt at a crossover was better than Strange New Worlds. A statement I don't much agree with. Firstly, I don't consider "Fissure Quest" to e a crossover, but secondly, I feel it's a bad crossover. Aside from the return of Lily Sloane to the franchise, the entire episode felt like a fanfiction fever dream. Most of the concepts felt like a group of Star Trek fans met up on a forum and started talking about what they would like to see.
"Oh let's put Garek and Bashir in a relationship!" "Oh, Trip's not dead and T'Pol and him are married!" "Oh, Henry Kim never gets promoted!"
It reads like bad fanfiction and came across as such. This is the issue with humor, it's subjective and bound to turn off a large amount of your fandom.
Strange New Worlds did it much better. It found a balance between the arrival of the characters from Lower Decks, making them feel complete. Not just like cartoon characters, like they feel in an episode of Lower Decks. They were given more onus and emphasis on less light-hearted moments. There was still some silliness, but it didn't feel like a fan's attempt to write their own Star Trek episode.
It felt like the series found the perfect balance between the Looney Tunes world of Lower Decks and the more conventional Star Trek series that is Strange New Worlds. I'm still not a huge fan of this crossover, as I felt it missed some of the marks I'd of liked it to hit, but as a whole, it's a much better viewing experience than Lower Deck's attempt.
So for that reason alone, it gets the tip of the cap.