英語候補being a fan ofpushing forbeing a supporter ofone's favourite (member of an idol group, character in an anime, player in a team, etc.)
推しカメラおしカメラ俗語fancamvideo recording in which the camera follows a specific member of an idol group during a live performance
箱推しはこおし俗語not having a favorite member of a group(being a) fan of an entire music group (esp. idol group)