There is some connection between Traditionalism and the "Traditional Islam" movement (also called Neo-Traditionalist Islam), though these are really different things (as explained in an earlier blog post). It is interesting, therefore, to see what is meant by "Traditional Islam" in a Russian context, given that there are Traditionalists in Russia, some of them Muslim. Answer, according to a new book, The Concept of Traditional Islam in Modern Islamic Discourse in Russia, edited by Renat Bekkin: no connection. A pdf of the book can be downloaded for free.
One of the best chapters in the book is the first, "In Search of ‘Traditional Islam’ in Tatarstan: Between National Project and Universalist Theories" by Leila Almazova and Azat Akhunov. As this chapter and other chapters in the book make clear, everyone knows what traditional Islam is not: it is not oppositional or Islamist. It is also clear that Traditional Islam is loyal to the Russian state. Beyond that, almost anything goes.
One observation by Almazova and Akhunov is especially interesting. "After decades of Soviet rule," they write, "Islam had virtually disappeared from social life in the Volga Region and had only been preserved in customs and traditions that were Islamic in essence and content but referred to as Tatar or Bashkir." Perhaps. It is widely agreed by scholars that religion and culture interpenetrate each other, but the emphasis tends to be on ways in which culture (and politics and so on) impact religion. Less attention is paid to the possibility of culture being a bearer of religion.
There may, however, be connections to Traditionalism that the contributors to this book have missed. Reference is made to the Tabah Foundation's role in organising the (in-)famous Grozny fatwa, and the Tabah Foundation is part of the international Neo-Traditionalist Islam movement that does connect to Traditionalism. See my "The Modernity of Neo-Traditionalist Islam," in Muslim Subjectivities in Global Modernity: Islamic Traditions and the Construction of Modern Muslim Identities, ed. Dietrich Jung and Kirstine Sinclair (Leiden: Brill, 2020): 121-46.