No nuclear threat, unless attacked with nuclear weapons.

No. Their official position is this:

According to a Russian military doctrine stated in 2010, nuclear weapons could be used by Russia “in response to the use of nuclear and other types of weapons of mass destruction against it or its allies, and also in case of aggression against Russia with the use of conventional weapons when the very existence of the state is threatened”. Most military analysts believe that, in this case, Russia would pursue an ‘escalate to de-escalate’ strategy, initiating limited nuclear exchange to bring adversaries to the negotiating table. Russia will also threaten nuclear conflict to discourage initial escalation of any major conventional conflict.

https://en.wikipedia.org/wiki/Russia_and_weapons_of_mass_destruction#Nuclear_weapons_in_Russian_military_doctrine

They annexed Eastern Ukraine, said it was part of Russia, then threatened “all means at our disposal” if anyone threatened Russia’s territorial integrity. Russia including Eastern Ukraine (and Crimea). Ie. if Ukraine made too many gains in Eastern Ukraine, they were threatening a nuclear strike.

This isn’t a secret. As mentioned above, it’s been official doctrine for years now and they keep making these threats. Wikipedia has a summary of some of them:

https://en.wikipedia.org/wiki/Nuclear_risk_during_the_Russian_invasion_of_Ukraine

For example:

Former Russian President Dmitry Medvedev, now deputy chairman of Russia’s Security Council, said that some Ukrainian military commanders were considering hitting missile launch sites inside Russia with Western-supplied long-range missiles. He did not name the commanders or disclose more details of the alleged plan and there was no immediate reaction from Ukraine to his threat. “What does this mean? It means only one thing – they risk running into the action of paragraph 19 of the fundamentals of Russia’s state policy in the field of nuclear deterrence,” Medvedev wrote on the Telegram messaging app. “This should be remembered,” Medvedev said. Paragraph nineteen of Russia’s 2020 nuclear doctrine sets out the conditions under which a Russian president would consider using a nuclear weapon: broadly as a response to an attack using nuclear or other weapons of mass destruction, or to the use of conventional weapons against Russia “when the very existence of the state is put under threat.” Medvedev made specific mention of point “g” of paragraph nineteen which deals with the nuclear response to a conventional weapons attack.

https://www.reuters.com/world/europe/russias-medvedev-warns-nuclear-response-if-ukraine-hits-missile-launch-sites-2024-01-11/

These are widely understood as nuclear threats in Russian media and by Russian audiences.