Wind droughts lasting a week or more are a 1-in-5 year event in the UK so, yes, must be accounted for.

Nuclear is prone to similar issues - statutory outages for inspections and refuelling, and emergency outages which often affect multiple plants at the same time (eg. a cracked steam valve in one plant requiring remediation on the same component in the others).

Keeping existing gas generators around, ready to be put into use when needed, is the simplest way of dealing with this until sufficient storage capacity is built out.