The ending of You Only Live Twice stops the SPECTRE plan to start a superpower war but leaves Blofeld alive, so the threat is not finished. In my opinion, that choice is the most interesting thing about the final act, because the film resolves the crisis and the villain separately.
The sequence runs in clear beats. Bond and Kissy Suzuki enter the volcano by a hidden route and free the captured astronauts. Bond is then caught by Blofeld, the moment the plan looks closest to working. Tanaka's ninja force storms the base, the assault Bond spent his time with them preparing for, and Bond kills Blofeld's bodyguard. Bond then disables the SPECTRE spacecraft before it can destroy another capsule, which removes the trigger for a US and USSR war. Blofeld sets off the base's self destruct and escapes, while Bond and Kissy survive and are rescued at sea as the volcano erupts behind them. Tanaka and the ninjas are picked up too, by Japanese and British forces.
The rescue answers the film's opening. In the first act the US blames the Soviet Union and the British suspect Japan. By the close, the war is stopped by a Japanese ninja force and a British agent working together, and Japanese and British forces pull them out of the sea. In my reading, the film settles the Cold War suspicion it started with through cooperation, not through a victory by one side.
Blofeld's own behavior explains how he gets away. Earlier in the film he kills Osato and feeds Helga Brandt to piranhas, so he punishes failure in others. When the base falls, he sacrifices the base and keeps himself. That is consistent with the character the film has built, though it is my interpretation of the scene, not a statement from the filmmakers.
Why leave Blofeld standing? My reading is that the film wants a villain it can reuse, since the story simply hands him back to later films. Donald Pleasence is billed seventh as Blofeld, and the character is the SPECTRE leader whose escape closes the plot without closing the threat. You Only Live Twice is the fifth film in release order, after Thunderball, and the next film in release order, On Her Majesty's Secret Service, picks up the series from there.
The scale of the finale is easier to judge with the figures. The Numbers lists a production budget of about $9.5 million, and the film took about $111.6 million worldwide, with about $43.1 million domestic per Box Office Mojo. The screenplay is credited to Roald Dahl and Harold Jack Bloom from Ian Fleming's novel, with John Barry scoring and Freddie Young as director of photography per TMDB credits. Those credits tell us who made the finale, but none of the sources say who shaped the Blofeld escape, so that choice is best read from the screen.
The title also invites a reading. Bond lives a second time because he fakes his death in Hong Kong in the opening act, then survives as the volcano erupts at the close. That is an interpretation, not a statement from the filmmakers. For where the film lands against the rest of the series, see James Bond movies ranked.