FILEPROPERTY not working over linked server to Azure SQL Database
Please note that logs are excluded for the purposes of determining database size in Azure SQL Database, that is the reason you receive NULL as result. You should add the following WHERE clause to your query.

WHERE type_desc = 'ROWS';


For example, the following query will work and won't return nulls.

SELECT 
SUM(CAST(FILEPROPERTY(name, 'SpaceUsed') AS bigint) * 8192.) 
AS DatabaseSizeInBytes,
SUM(CAST(FILEPROPERTY(name, 'SpaceUsed') AS bigint) * 8192.)/1024 /1024
AS DatabaseSizeInMB,
SUM(CAST(FILEPROPERTY(name, 'SpaceUsed') AS bigint) * 8192.)/1024/1024/1024 
AS DatabaseSizeInGB
FROM sys.database_files
WHERE type_desc = 'ROWS';