I am currently using the Neo4j Community Edition 5.10 installed via Azure Marketplace. How can I update it to version 5.11?
You should be able to follow the Neo4j migration guide. There shouldn't be anything special to worry about with Azure, and Community Edition is a standalone instance (not a cluster). I've included the link in our docs for migration: Upgrade or patch Neo4j 5 - Upgrade and Migration Guide.
Hope this helps!