Not the sheltered, yeshivish version of reality you grew up with…
Lemaaseh, the situation today is fairly straightforward. Rav Shternbuch has one known tallis katan with Techeiles—the pair prepared for him by Rav Yechezkel Toporovitch—and he wears it sometimes. At his present advanced age, however, he is dependent on others to bring him his tzitzis in the morning. His son Rav Chaim Ozer wears Techeiles and is supportive of his father wearing it, while another son, Rav Osher, is opposed. In practical terms, which pair Rav Shternbuch wears on a given morning can depend upon which son is getting his tzitzis for him that day.
The important distinction is that Rav Shternbuch’s personal practice should not be confused with a public psak that others should wear Techeiles. His earlier opposition clearly softened after he looked into the issue further, he obtained a Techeiles tallis katan of his own, and he has worn it on numerous occasions. Nevertheless, he has not instructed others to wear it and has even continued, at least at one stage, to say that doing so was not advisable.
In short: Rav Moshe Shternbuch has a tallis katan with Techeiles from Rav Yechezkel Toporovitch (who happens to have also been born in Great Britain like R’ Shternbuch, having lived there for eight years), wears it sometimes, and is no longer opposed to Techeiles as he once was—but he has not told others that they should wear it.