Arun Sirpal takes us through Azure SQL Database Serverless:
This is best used for those single databases that are ever changing with unpredictable patterns. With the concept of being billed per second (based on the vcores used) rather than per hour means that pricing can become more granular especially now with auto-pause becoming possible. The auto-pause delay defines the period of time the database must be inactive before it is automatically paused (only charged for storage). You should only use this if you can afford some delay in compute warm-up after idle usage periods, otherwise it is best to stick with provisioned compute tiers ( classic tiers).
I could see this being useful for dev or test databases, or maybe a personal site with heavy external caching.