According to the current nuclear doctrine of Russia, is the transfer/usage of shells containing depleted uranium considered as a nuclear attack on Russia? Technologically, can it be considered as a radiological weapon or dirty bomb? I am not interested in what Putin or Medvedev say on the TV, but the official Russian doctrine. Is any specific countermeasure for such a weapon mentioned in it? If they interpret it as an attack with a dirty bomb, let's say, via a political decision, what are the countermeasures according to the doctrine?
Well, to flip the question somewhat, Russia fields the Svinets-2 APFSDS which ...drumroll... holds DU.
Russia has further developed its DU munition. According to an article of TASS news agency (based on a statement of the Russian Ministry of Defense), Russian T-80BV tanks are now to be equipped with such high-penetrating ammunition. The article states that tanks of the T-80BV series got the new gun 2А46М-4 with an improved stabilizer and the loading mechanism for the ammunition 3BM59 Svinets-1 and 3BM60 Svinets-2. The ammunition of the type „Svinets“ (English: „lead“) is a part of Russian arsenal since 1991: „Svinets-1“ has a uranium-tungsten carbide core and „Svinets-2“ uses depleted uranium.
More techy info (pdf):
But, let's get it from the horse's mouth, (2018), Russia’s upgraded T-80BV tank to feature capability of firing depleted uranium shells - Military & Defense - TASS:
The information that one of the shells has the depleted uranium core was confirmed to TASS by military expert, Editor-in-Chief of the Arsenal of the Fatherland journal Viktor Murakhovsky. "It has the alloy of the depleted uranium and tungsten," he said, adding that the open sources mentioned it as "the Material B."
The use of depleted uranium ammunition does not violate any international treaties, the expert said.
To bring this back to the question. DU ammunition, is very much part of Russia's conventional weapons doctrine, since they deploy it in that role themselves (DU is used for its ballistic and armor penetration properties, not because of "nuclear stuff").
How they will react to the use of NATO-supplied DU shells can't be answered at this point since it would be purely speculative. Consider this another one of the Kremlin's red lines, for whatever that is worth. However, they will have a hard time convincing anyone sitting on the fence of their good faith if they retaliate with nuclear/chemical weapons because of it: DU is considered as conventional, if controversial, armaments by most countries, including themselves. Not as "dirty bombs".
Also, keep in mind that, while countries may have contingency plans to handle dirty bomb events, those would, I assume, typically be concerned with terrorist attacks. Dirty bombs don't make all that much sense in the context of high intensity conventional war, so expecting "doctrine" covering those circumstances, and us knowing about it, is unrealistic.
It doesn't matter what their official policy is. It only matters what they try to sell to the rest of the world.
They showed their little kidnapped children to try and sway the world into thinking they are the good guys. The ICC slapped Putin with war crimes. PR message gone terribly wrong :-D. Does this seem like a rational stance?
Why would they not portray DU shells as a nuclear attack to justify their own nuclear response? Too often we get hung up in the words people say and official written policies because we feel like they are being rational and they can be reasoned with. They've been attacking Ukraine for more than 12 months for no rational reason. Why do they need one to justify an escalation?
Just like the US attacked Korea and Vietnam to "deter communism" and overthrew countless Latin governments for the same reason. Those weren't rational decisions nor rationally justified. But the fed the US public their "rational" justification (if they even let them know it was going on).
The question misses the point because it assumes Russia is doing this for rational reasons. And they aren't. Maybe they feel like they are being rational, but so did the US. But clearly to a neutral 3rd party both aggressors were out of their mind.