Just because a show was developed for, or even by, a specific performer does not mean it’s a “vanity project.” Musicals have been developed for specific performers since the inception of the form.
A vanity project is typically intended as a showcase of somebody’s perceived multi-hyphenate abilities. It’s somebody writing, directing, designing, producing, and starring. Burlesque became a vanity project for Todrick Hall, who is starring, writing, choreographing, and directing, for instance.
"...everyone finally shut up, and the audience could enjoy the beginning of the Anatevka Pogram in peace."