Self-serious

This is not to say that there is a self-serious bone in Bill's body. He's a kid on a trike with a slingshot and a peashooter -- always has been, always will be.

Source: wiktionary

Elizabeth had never recorded any period of her existence, failing to grasp the point of an exercise so self-absorbed and self-serious.

Source: wiktionary

New Age is goofy, yet self-serious, with no sense of irony.

Source: wiktionary

Relatable in neither its bizarrely specific plotting nor its broadly generic emotions, Dear Evan Hansen is so self-serious that it almost plays like self-parody, only without any “so bad it’s good” fun. We may all be striving for human connection right now, but we’re unlikely to find any here.

Source: wiktionary