ujm – A large portion, indeed likely well over a majority, of current fully Torah observant Sephardim, are religiously observant under Ashkenazic influence. This includes them (or their parents/grandparents) having attended Ashkenazic Yeshivos, etc.
This is a complicated and sensitive subject, and the breakdown of the numbers depends entirely on how you define “fully Torah observant”. If you use an Ashkenazi Chareidi definition, then that’s called a “No True Scotsman” argument. (No Scotsman ever ran away from battle. Aye, Donald MacRonald did run away? He wasn’t a True Scotsman… = No truly observant Jew wasn’t influenced by Ashkenazim, because anyone who wasn’t influenced by Ashkenazim isn’t a truly observant Jews.)
If you define “observant” as Shomer Mitzvos in the basic sense, which is what most Sephardim were to begin with, then the vast majority cannot be credited DIRECTLY to Ashkenazi influence. (More on that below.)
ujm – A lot of this is the result of the Ashkenazic Torah world having strongly helped their Sephardic brethren remain strongly Torah observant during their transition from the Arab lands to Israel, when the State of Israel spent considerable resources in attempts to secularize the Sephardic immigrants.
This is very true, however unfortunately the number saved were dwarfed by the number lost. The entire Torah world then, less than five years after the Holocaust, was a small and impoverished ????? ??????, and not in a position to compete with the Mapai bosses, the Jewish Agency, the ???? ????? Kibbutz movement, and other ?????? who played a role in the Shmad.
What did happen, somewhat later on, is that many Sephardi parents who kept their Mesorah of ???? ????, realized what was going on, and with great ?????? ??? sent their children to Yeshivos, which mostly (though not exclusively) were Ashkenazi. Usually Litvish, some Chabad. Those children in many cases grew up to become ?????? ????? who opened their own Sephardic Yeshivot and Talmud Torah, and were ???? the next generation of Sephardi children, including many who didn’t come from observant homes at that time. There were also Sephardi ????? who learned ??????? in the old Sephardi Yeshivot, such as Rav Ovadia and others, who sent their children to Ashkenazi Yeshivos, and they eventually opened Sephardi Yeshivot that synthesized some elements of the Ashkenazi Derech in learning. Rav Meir Mazuz ????, who recently passed away, learned by his father in Djerba, then in a Lubavitcher Yeshiva opened in Tunisia, where he became Rosh Yeshiva, and then he opened a Sephardi Yeshiva in Bnei Brak where he was ????? to follow the Tunisian ??? ??????.
While all of this was happening, many if not most Sephardim remained basically ????? ????? to some extent, despite the best efforts of the Zionists. They built Shuls which the vast majority of them attended, and they maintained their Minhagim and distinctive sincerity, Emunah, and legendary respect for ?????. The products of the various Yeshivos mentioned became Rabbanim, Mechanchim, and Kiruv workers, who helped significantly raise the level of ????? ?????? and Torah learning among the Sephardim at large over the last 40 or so years, so now it is much more common to see Sephardi Baalei Batim who are truly learned and ??????? ??????. It is also important to note that Sephardim typically see the entire community as an organic whole, where everyone feels they belong even if not everyone is on the same level of observance, so it would be very hard to do an accurate breakdown of the numbers.
So, bottom line, it’s true that the ?????? ??? of the ?????? and others eventually bore fruit, and there is an Ashkenazi connection to much of the contemporary Sephardi Torah world, through different channels, most of them indirectly.