All these expensive projects are going to be their economic downfall. Keep in mind in OTL, Germany's obsession with wonder weapons took incredible resources that could have been better used in the Eastern Front. Wonder weapons too are not enough to stem the tide of the war.Ooh, thanks for that! I'll have to check it out.
By the 1990s/2000s (my rough prediction for when things come to a head) the Allied powers that Nazi Germany would be facing off against when they decide it's time for the Endsieg would certainly be as prepared as one can be for that eventuality. Nearly all of them would likely be more militarized than OTL, in both conventional weapons and WMDs, and with a large and heavily militarized presence in space (no bilateral arms agreements or Outer Space Treaty in this world; Germany had shown with its behaviour that it can't be trusted to uphold anything). They've likely gone all-in on the SDI idea. Britain and Ireland, being right on the frontline, probably have extensive systems of fallout shelters and an Iron Dome-like antimissile system (looking like a combination of Israel and Switzerland).
But even so, there's only so much you can do to prepare for an all-out war with WMDs, and none of it can guarantee survival or is immune to being countered. Nazi Germany certainly can't win a war they start at this time (even if they can easily make themselves believe they can), but both sides can certainly lose.
In this Axis Cold War, the Reich would have been a big pariah anyway (just like a bigger North Korea, even the USSR wasn't a pariah despite its authoritarian faults) with the whole Free World against them. Once this Axis Cold War turns hot, it would probably resemble a 1960s nuclear exchange where one side is hurt but the world isn't a wasteland like in most 1980s scenarios. A nuclear program would cost Germany precious resources in which it has limited access to, while the U.S. and the UK would have both the resources and the minds to create functional devices before Germany could catch up.