An Azure relational database service.
Azure SQL Database offers a feature called "Pause and Resume" for its serverless tier.The cost for a serverless database is the summation of the compute cost and storage cost.But this approach is quite expensive.
Or you could just set up a MySQL database on a virtual machine and use automation tools (logic apps) to start/stop the VM based on a schedule or triggers.
Another alternative you can try is that if you have multiple databases with varying and unpredictable usage patterns, an elastic pool might be more cost-effective than individual serverless databases. It allows you to share resources among multiple databases.