There is no mobilisation (source)
Russia has 2,000 tactical weapons, in very many shapes and sizes for use on land, sea and air. The weapons are not deployed on missiles or aircraft, but kept in bunkers in storage sites dotted around Russia. There are 12 national storage sites, known in Russian military parlance as “Object S”, one of which is in Belgorod, right on the Ukrainian border.
There are also 34 “base-level” sites, closer to the delivery systems. In a time of crisis, warheads would be moved from national to base-level sites – and up to now western intelligence agencies say no such movement has been observed
Sources in the question talk about a train carrying that looks more like conventional weapons (canons) and the submarine carrying nuclear weapon delivering drone left its base in Arctic circle but this is still far and Turkey unlikely to let it into Black Sea. If they plan to strike with underwater drone, what would be the military target? Ukraine has no notable fleet so no large military ports.
These may be just ordinary movements, while if they only plan to detonate a single warhead for the demo, no mobilisation would be necessary.