The character of Eve Teschmacher has had a weird trajectory. She was created for the 1978 movie and appeared only in it and its sequel, then nowhere else for the next 20 years. But then versions of her started appearing infrequently in the comics from 2000 onward, then Tess Mercer in Smallville was loosely based on her (but was later retconned into being a version of Lena Luthor), then a new version of Eve was introduced in Supergirl 36 years after her previous screen appearance and became a major recurring character. And now her appearance in this movie is being announced as if she were a familiar core Superman character as much as Jimmy Olsen.
It's weird how some characters created for comic-book movies/TV take off and get reused in other adaptations, while others are forgotten. Eve Teschmacher gets a new lease on life, Phil Coulson gets his own TV spinoff, Harley Quinn has become so big that the Joker and Batman are supporting characters in her star vehicles, and of course Jimmy Olsen and Perry White originated on radio. But aside from the occasional use of the "Jack Napier" name for the Joker, we've never seen a new version of any of the characters created for the Burton Batman movies, like Alexander Knox (though the original had a cameo in the Arrowverse Crisis), Carl Grissom, Bob the Goon, Detective Eckhardt (though he was basically a more corrupt Bullock), or Max Shreck. Nor have we ever gotten alternate versions (outside Arrowverse doppelgangers) for most of the characters introduced in the 1990 The Flash TV series like Julio Mendez, Megan Lockhart, Captain Garfield, Officers Murphy & Bellows, Fosnight the informant, etc. (although it looks like Richard Belzer's TV-reporter character Joe Kline has a comics counterpart in a story written by the show's creators).
As far as the Burton movies, I don't think any of those characters were really very memorable other than Eckhardt and Shreck and I wouldn't really expect most people to use either of them. Eckhardt is too close to the already well-known Bullock, so what's the point of bringing him back? And Shreck, while very unusual and memorable, is such a quintessential Burton character that he wouldn't fit right in any version of Gotham that isn't fully committed to the Burtonesque style world.