Hi Helge,
I don't think shared disk is what you want for your use case. Shared disk is typically used for cluster workloads. For example, SQL Server Always On Failover Cluster Instance, Hyper-V failover cluster, scale-out file server, etc. You would install Failover clustering on the servers, create cluster, cluster shared volume, servers would all need to be same version, etc.
Windows Failover Clustering manages which node writes to the disk so there aren't problems.
As an alternative, have you considered creating an Azure Files share that you could access from both servers?
Please click Accept Answer and upvote if the above was helpful.
Thanks.
-TP