You are very much on target. Just one correction. "Kinzhal" missile that Russia promotes as their hypersonic wonderwaffe is not in fact that.
"Kinzhal" is a slight modification of standard Russian "Iskander" ballistic missile allowing it to be launched from a plane (specifically an intercepter fighter jet MiG-31).
As with most ballistic missiles, the warhead flies a part of its trajectory at a hypersonic speed, but has to slow down at the final part of its trajectory. It is just as hard (or easy) to intercept as any other ballistic missile.
Mounting it on a plane gives it a longer range, and potentially makes it harder to be destroyed by a pre-emptive strike (although experts disagree on this).
Traditionally the term "hypersonic weapon" is used for very different class of weapons. Basically, a true "hypersonic weapon" is something able to maneuver while flying at hypersonic speeds, and able to maintain this speed all the way to the target. "Kinzhal" is nothing like it.
So it is not some fantastic wonderwaffe making NATO air defenses suddenly useless. It presents some additional challenges, but nothing drastic.
What makes possible nuclear war with Russia really dangerous is just the number of "conventional" ballistic missiles Russia has. In theory Russia may launch thousands of rockets carrying tens of thousands of warheads, and no air defense has any hope to intercept all or even most of them.
This is the same as it always was. The difference with Soviet Union is that Soviet leaders appeared to be afraid of a world suicide, and Russian leadership appears (or wants to appear) to be crazy and ready to destroy the world.