DB instances in this cluster has a size that isn't compatible with Aurora global databases.

The error message you're encountering is related to instance size compatibility when setting up an Aurora Global Database. While there isn't explicit documentation stating a specific instance size requirement for Global Databases, there are some important considerations to keep in mind:

1. Aurora Global Databases have certain performance and replication requirements that may not be fully met by smaller or burstable instance classes like db.t3.large.

2. Generally, for production workloads and features like Global Databases, it's recommended to use more robust instance classes from the R5 or R6g families, which are optimized for database workloads.

3. The db.t3 family, particularly smaller sizes, may not provide the consistent performance needed for Global Database replication across regions.

To resolve this issue and set up an Aurora Global Database, you might need to:

1. Upgrade your instance class to a larger size, possibly within the R5 or R6g family. For example, you could consider moving to db.r5.large or db.r6g.large.

2. If cost is a concern, you could explore using db.r5.large or equivalent for the primary instance and potentially keep smaller sizes for read replicas in secondary regions.

3. Review your workload requirements and choose an instance class that can handle your performance needs as well as support Global Database functionality.

Remember that while changing instance types, ensure that the new instance class is compatible with your Aurora MySQL version. Some older instance types may not be supported in newer Aurora versions.

Before making any changes, it's advisable to test the new configuration in a non-production environment to ensure it meets your performance and cost requirements while supporting the Global Database feature.
Sources
Aurora Global Databases | AWS re:Post
Aurora cluster, DB Instance class for my region | AWS re:Post

Unfortunately, our public documentation on this could be a little more definitive but at the link below [Ref 1], the section on "Configuration requirements of an Amazon Aurora global database" says:

DB instance class requirements – An Aurora global database requires DB instance classes that are optimized for memory-intensive applications. For information about the memory optimized DB instance classes, see DB instance class types. We recommend that you use a db.r5 or higher instance class.

Aurora Global Databases require more resources to support the cross-region replication architecture so burstable-performance instance class types are not supported. You can choose among all the other supported instance class types including Aurora Serverless v2 which can scale up & down vertically in small grain increments. In addition, Secondary Regions in a Global Database could also be "headless" (i.e., only a storage volume without any compute instance) to save costs although the tradeoff is higher RTO if you need to failover to it in a DR event because a compute instance needs to be provisioned first. See the docs in [Ref 2] for more details.

[ Ref 1 - https://docs.aws.amazon.com/AmazonRDS/latest/AuroraUserGuide/aurora-global-database.configuration.requirements.html ]

[ Ref 2 - https://docs.aws.amazon.com/AmazonRDS/latest/AuroraUserGuide/aurora-global-database-attach.console.headless.html ]