Around this time, the Burya was shelved in favor of an ICBM. Fittingly, it was a Korolev design, the R-7, or SS-6 Sapwood, that was selected. In modified form, this missile was used to launch Sputnik 1, the world's first artificial satellite, into orbit, and was used for an entire family of Soviet, and later Russian, space launch vehicles.
Remarkably, it seems that Western intelligence entirely failed to identify the Burya missile, a point raised by Steven J. Zaloga in his book The Kremlin's Nuclear Sword. Whether that's true, or whether it was known about, but not fully understood, it apparently never received a Western reporting name or designation.
In some ways, of course, the story of the ground-launched strategic cruise missile has now come full circle in modern-day Russia, with the development of the notorious 9M730 Burevestnik, although this trades supersonic performance for, reportedly, almost unlimited range, on account of its nuclear propulsion. You can read more about recent developments in this project in this previous War Zone article.
The mystery that surrounded the Burya makes the appearance of this 1959-vintage film all the more interesting. It is to be hoped that the Russian archives will continue to reveal such insights into more of the Cold War's hidden military history.