I believe that the military effects of any deployment take third place in the Russian reasoning, less important than messaging to the Western 'elites' and general public.
I could be wrong on that, just as I believed too long that the ground force deployments one and a half year ago were posturing, but I see no tangible military benefit for a Russian forward deployment. The mirror-image NATO nuclear sharing collects policy input from some non-nuclear NATO members, and spreads the responsibility for decisions to them. I don't see a similar outcome between Russia and Belarus.
Policy 'elites' would note the strong signal if weapons actually move and there is not just talk.
Early in the Cold War, there was a phase of rapid expansion of nuclear arsenals. The US and the Soviet Union deployed tens of thousands of them. The UK, France and China became nuclear powers and deployed hundreds (not enough for MAD, but enough 'to matter' in the decisionmaking of any rational government).
Later in the Cold War, the US and the Soviet Union decided to stabilize the arms race. They agreed to limits on total numbers, on types of weapons, on deployment locations, on readiness.
With the fall of Communism, the US and Russia agreed to much more significant cuts in the numbers, locations, etc. For years, it looked as if the size of the arsenals was on a downward trajectory. The deployment concepts were less to consider nukes actually employable, and more to see them as an insurance policy. A move away from 'tactical' doctrine, towards an exclusively 'geostrategic' one.
In recent years, this trend has been reversed. Various US administrations have looked at hardened bunker-busters, for instance, and Russia wrote a nuclear doctrine which envisions nuclear use against an overwhelming conventional attack. (NATO used to have a similar doctrine, but people thought it had been 'overcome' with the post-Cold-War agreements. It isn't absolute capabilites, but the direction of change and rate of change which matter.)
But the main reason is this:
The audience is not nuclear strategists. It is a public which is ill informed about nuclear matters.
And because it is ill informed, yet concerned, the public is going to overreact to each new nuclear threat until repetition wears it out.
Back during the Cold War, the joke was that to learn about nuclear arsenals, one could ask a general or a peace activist. The general would know exactly but not tell, the peace activist would have a pretty good idea and tell you. This was a pre-internet era, when one could not google things like Reflex Action or SIOP. Yet peace activists tried to learn and understand what it means.
Most people today simply have no idea what nuclear weapons mean. Remember the recent G7 summit in Hiroshima? Not a post-apocalyptic wasteland, and it has been green and habitable for many years. So Russia has 'media figures' talk about nukes, and it has officials talk about nukes, all to raise anxiety and to reduce Western support for Ukraine. But they cannot simply repeat the same words over and over again, so they have to tell something new.