Do I Need an Islamic Divorce After a Legal Divorce If My Husband Refuses to Give Talaq?

Assalamu Alaykum. My husband and I have been separated since March 2023. I asked him for talaq multiple times, but he refused and said I should apply for a legal divorce first, after which he would give talaq. I applied in May 2023, and in June 2023, he responded, "The respondent will continue without disputing the divorce." We reconnected in July 2023 while the divorce proceedings were ongoing but separated again in November 2023. The divorce was finalised in June 2024. Now, despite his promise to give talaq after the legal divorce, he refuses, claiming it’s unnecessary since we are legally divorced. He is still trying to reconcile, but I don’t want to. I just want a clear talaq. My questions are: Is the divorce valid Islamically? Am I Islamically divorced? Do I still need an Islamic divorce if we are legally divorced? I’ve read that signing the divorce papers might count as talaq, but I’m unsure if our brief reconciliation affects this.