I think the current arms race started in 2002 when the US pulled out of the ABM, followed by the "upgrades" which started under Obama. (The research for those upgrades of course started long before - it's the deployment I'm interested in.)
I think adding super-fuze to US nuclear weapons - "In the case of the 100-kt Trident II warhead, the super fuze triples the killing power of the nuclear force it has been applied to. https://thebulletin.org/how-us-nuclear-force-modernization-u... - is an example of not just of the "mere existence of a nuclear arsenal", but a determined effort to tilt the balance very much in favor of the US.
Why did we need that upgrade?
I think the US has developed its systems far enough in that direction that Russia is now forced to spend money to keep up, as otherwise MAD is no longer effective.
And that's why I call it an re-uptake of the arms race.
What would you expect to see if there were a new nuclear arms race?
There are about a zillion reasons you can come up with for that, to match the entire spectrum of political outlooks and levels of cynicism, none of which have to include 'to start a new nuclear arms race'.
What would you expect to see if there were a new nuclear arms race?
Well, for one thing, I'd expect the race to include at least two parties. If Russia truly believed something on the US side is actually putting the global strategic nuclear balance in question, I imagine their response would be more robust than running a missile-naming competition on the internet.
The reporting on these issues always stresses the risk of starting a new nuclear arms race - the NYT piece you linked to does, as has much of what has been written over the last 15-odd years at least. The risk is surely real but this does imply that we have not, in fact, been in a nuclear arms race. So far.
Because I can't think of any.
You mention wanting something "more robust than running a missile-naming competition on the internet". How does the RS-28 Sarmat not count as one example? Quoting from https://www.globalsecurity.org/wmd/world/russia/ss-30.htm :
> On 07 September 2016, a defense industry official told Russian media that the mass production of the RS-28 Sarmat intercontinental ballistic missile, a new multi-warhead, super-heavy missile designed to defeat anti-missile systems, would begin in 2018, two years ahead of schedule. ...
> Russia's State Rocket Center V. P. Makeyev of (Miass) and NGO's Engineering (Reutov) along with NPO Mashinostroyeniyais is developing the new sarmat / Sarmatian heavy liquid-propellant intercontinental ballistic missile to overcome the U.S.’s prospective missile defense system, Strategic Missile Forces chief Lt. Gen. Sergei Karakayev said 16 December 2011. The decision had been made to create a new silo-launched heavy missile that will have “enhanced capability to breach a hypothetical US missile defense system,” he said.
That's exactly what I would expect as part of a nuclear arms race, as a response to US efforts to get ahead in the race.
Do you even know how old American missiles are? They are from 1970-80s. US made no new developments here since 1991, when all ICBM programs were canceled.