I'd advise looking into laws about copyright and fair use and derivative works. You're not the first person to make a homage character or a pastiche. I would advise setting a bunch of "show within show" style franchises within your own universe that can clearly take inspiration from another work but have their own in universe lore. For example, Marvel has a team of characters called "The Squadron Supreme" each with their own unique backstory... however, it doesn't take a lot to realize the characters analogs to DC Comics superhero line up "The Justice League" and the team exists so that the Avengers can "fight" the Justice League.
Another example comes from the Japanese show "Kamen Rider" and their season Ex-Aid which focus on a group of four doctors who are also superheroes. The villains of the season have created a biological disease that will allow video game bosses to manifest into the real world by using the infected subject's bodies, killing them in the process. The four heroes fight using a system that allows them to turn into a hero that uses abilities of different player characters from video games to combat the manifested monsters. All of the games are clearly Homages to real classic video games, but they are real games within the setting of the universe (The titular hero is an homage to various platforming games, with Mario being the most obvious.). Another hero is based on a line of Fantasy RPG games that have Legend of Zelda vibes. A Third is based on First person shooters and a fourth is based on racing games.
For a more English accessible event, the film Galaxy Quest doesn't even attempt to hide that the titular TV Show is clearly taking designing cues from Star Trek, but the show in question is a show in show... the film's central plot is that real aliens that had no concept of fiction and believed the show was historical documents... and have enlisted the actors who played the characters to help them in a real interstellar war with a real alien overlord. Similarly the real life sho "The Orville" would debut some decades later, which posited a universe similar to one of Star Trek... but the heroes we follow act and behave like they are in a workplace comedy... that just happens to be on a real space ship that runs into problems worthy of the U.S.S. Enterprise.