So I don’t read any Magic Kaito... but does Conan/Shinichi show up as often in Kaitos manga as Kaito does in Detective Conan?
Conan himself doesn't appear but Shinichi does appear in the Black Star heist (ch23). This was before Shinichi turns into Conan and is a flashback for Kaito on the day he meets Conan (hence the name, though I think I would have preferred if we had the actual heist in Kaito's perspective) There are also references that are made that allude to Conan and the DC side.
Phantom Lady heist's whole case is the direct prequel to the Sakamoto Ryouma case in Conan. Writer's side words "What's this about Sakamoto Ryouma's 3 piece set? Check chapter 731-733 in Detective Conan!"
In Kaito Corbeau's case, there was mention of Advisor Suzuki who is of course comes from Conan
and Sun Halo has the contraption that looks eerily similar to Samizu Kichiemon's machinations (ruthless punishment traps that has a fan at the end to mock you. Pretty much a repeat of Iron Tanuki)