I'm generally happy for characters from my comic to appear in a background cameo in a panel or two, but that's generally as far as I'd go in most cases.
I often find crossovers where the characters are from series written by different people disappointng because if it's written by the writer of one of the series, the characters from the other series tend to feel like fanfic versions of themselves, and if it's written by a third party, sometimes everyone feels like a fanfic version of themselves.
And then there are the issues where each party involved obviously wants their characters to be seen in a light that makes their series look good, so there usually needs to be a story where everyone is equally cool while still showing the reader what they want to see, like the characters fighting together, fighting each other, solving a mystery etc. So that's often an issue when the characters have vastly different power levels.
Honestly the way Kingdom Hearts treats Selphie is a prime example. Selphie in Kingdom Hearts is an airheaded romanticist. If you've only paid vague attention to stuff about Final Fantasy VIII, you might well think that, and I've seen her depicted in fanfics that way. If you've actually played FFVIII and regularly interacted with this character, you'll know that Selphie has kooky mannerisms (often as a coping mechanism for her really quite tragic life) and often seems a little oblivious and innocent, but she's deceptively smart and cunning; able to fly a space ship, invent social media in her world and come up with a pretty effective plan to infiltrate and sabotage a military base.
In the same way as KH depicts Selphie Tilmitt in a way that really doesn't get across what a fun and multi-faceted character she is, I'd be really worried about handing over characters from my comic to a crossover. I don't want to see like... Subo as literally just a stupid himbo punching bag, or Rekki reduced to just a cocky girlboss, or Jules turning into literally just Entrapta from She-Ra.
I'd have to really trust a writer and feel like they really "get" my characters to put them in somebody else's hands, and I'd also want the crossover to have some smart way of dealing with the relative power level of Errant (and especially the most powerful characters like Rekki and Crow) and whatever they crossed with, whether it was a setting with a lower power level (more Lord of the Rings or Game of Thrones level) or one with a higher power level (Gurren Lagann level).