Edit 2023-12-21:
It would seem our wait is coming to an end!
EDIT 2024-07-09: We finally have it, guys, all major regions!
https://aws.amazon.com/about-aws/whats-new/2024/07/amazon-rds-data-api-aurora-postgresql-additional-regions/
The post says Postgresql v15 only, but v16 is supported too!
https://docs.aws.amazon.com/AmazonRDS/latest/AuroraUserGuide/data-api.html#data-api.enabling.modifying.all
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The Data API was included in Aurora Serverless v1 have connected it to AWS AppSync as a resolver.
With v2 this is no longer an option, and users are stuck on v1 (with its inadequate scaling), or presented with the option to add Lambda as resolvers, which not only takes time to develop, but also adds latency and maintenance to the solution.
Several requests have been made for adding the Data API to v2 through AWS support, but so far it has not been added.
Per an unspecified AWS resource of mine, the Aurora team does not plan to add the Data API anytime in the near future, if ever. It is not a planned feature for v2 (nor v3, as that is on the drawing board, apparently) which would mean that it is not happening within the next 6 months at least.