I think in general in this model you would either use a cluster of DB servers where you can also spin up more as needed, or use the cloud vendor's dedicated SQL services, ie: Amazon RDS (https://aws.amazon.com/blogs/database/scaling-your-amazon-rds-instance-vertically-and-horizontally/ ) or Microsoft Azure's solution: https://docs.microsoft.com/en-us/azure/mysql/concepts-service-tiers
It looks like in both cases you can scale up to a bigger server pretty easily.. Azure mentions 4-30 seconds downtime to do so.