Is it permissible to offer expiation for a vow to abandon watching movies and anime for life by watching anime only?

The statement "O Lord, I promise You" is a promise. If it is intended as merely a promise, then fulfillment is not obligatory. However, if it is intended as a vow (nadhr), then it becomes a binding vow. Watching anime and movies is permissible if they are free from شرعي (Shari'ah) prohibitions; otherwise, they are forbidden. If you did not intend a vow with your promise to watch permissible anime, then nothing is incumbent upon you. But if you intended a vow to watch permissible anime, then according to the majority of scholars, an expiation for breaking an oath (kaffarat yameen) is not obligatory upon you. As for forbidden anime and movies, watching them is absolutely impermissible. If you had intended a vow to abstain from them and then watched them, an expiation for breaking an oath is not obligatory upon you according to the majority of scholars, because a vow to perform an obligatory act is not considered valid by them.