This provides a view on Russian nuclear doctrine which might allay some fears.
https://sgp.fas.org/crs/nuke/R45861.pdf
These two sections are concerning:
These revisions have led to questions about whether Russia would employ nuclear weapons
preemptively in a regional war or only in response to the use of nuclear weapons in a broader
conflict. In mid-2009, Nikolai Patrushev, the head of Russia’s Security Council, hinted that
Russia would have the option to launch a “preemptive nuclear strike” against an aggressor “using
conventional weapons in an all-out, regional, or even local war.”
As with previous official statements, this document does not call for the preemptive use of
nuclear weapons during conventional conflicts. But it does not completely resolve the question of
whether Russia would escalate to nuclear use if it were losing a conventional war. It notes that,
“in the event of a military conflict, this Policy provides for the prevention of an escalation of
military actions and their termination on conditions that are acceptable for the Russian Federation
and/or its allies.” Analysts have assessed that this means Russia might threaten to escalate to
nuclear use as a way to deter a conflict that would threaten the existence of the state.
Patrushev is the one closest to Putin.