ZSK said – What would be called old-school Sephard/Edot HaMizraḥ – meaning the pre-Zohar/Kabbalah Geonic and Rishon eras (figures such as Rasag, Ibn Ezra, Rambam, Radaq, Ibn Ghayyat, Ibn Janaḥ, etc.) are a completely different world from Chassidus.
At least now I understand what you meant, but the thread was about Sephardim living today. The Sephardim post-1492 abandoned philosophy almost entirely, for the reasons why see the works of the Hassid Yaabetz (another great Sephardi early Acharon…) who was among those who left Spain. There were Sephardi Rishonim who also differed (in a major way) with the school of thought you mentioned such as: Raavad, Rashba, Rabbeinu Yonah, Ramban, R’ Yosef Gikatila (שערי אורה), R”I Sagi Nahor, R”I d’min Acco, and more. The Geonic era was essentially prior to the Sepharad – Ashkenaz divide, although the debate over philosophy existed already then.
Be that as it may, since the Baal Shem Tov HaKadosh and the Ohr HaChaim HaKadosh (and the Chida who already noted the connection between them) there has been positive interaction between Sephardim and Chassidus, in both directions.