If you reach the maximum storage, you might get Message 1105 for a managed database or Message 1133 for the instance.
Just like SQL Server, the size of any new database will be based on the size of the model database. The model database is a 100-Mb data file and an 8-Mb log file. Also like SQL Server, the size of model is configurable. You can alter the size and the number of files, but you don't have control over the physical location of them. Microsoft has commitments on I/O performance based on your deployment choice. Additionally, because remote storage is used in the General Purpose service tier, the data file and log file size can affect performance.
For Azure SQL Database, there is a possible maximum size of database files based on your chosen SLO. You choose a Data max size up to this possible maximum size. Maxsize for database files (as defined by the sys.database_files.max_size column) can grow to Data max size.
The Azure SQL Database Hyperscale tier is different from the other service tiers in that it creates a database that's initially 40 GB and grows automatically in size to the limit of 100 TB. The transaction log has a fixed size restriction of 1 TB.