SQL Server AlwaysOn Availability Groups Cluster File Share Permissions
HA cluster - does each server node within the cluster need access to that file share or is it just the cluster name that needs write access to the file share?

Each node participating in WSFC should have access to the FS witness and the WSFC name or cluster name object( CNO) should have read write permission on fileshare folder and also at NTFS level.
A FS witness should not be part of WSFC and can reside on &quot;any&quot; windows machine which is accessible to both the nodes. Please note that the file share witness should reside on one of the machines which is part of domain in which WSFC is created.