Database connections do not close using RDS Serverless v2 and Data API

I am using Drizzle with a RDS Data API connection to a Serverless V2 PostgreSQL cluster. I've now started consuming some events and a particular heavy influx of events caused a few hundred Lambda function to be spun up and connecting to the database. However, even after they are all done, the RDS resource is still unavailable since it still sees all those database connections as open. The only solution I had was stopping and starting the cluster again. In a second test, I explicitly close the the RdsDataClient, but no cigar. Any tips on how I can get those connection properly closed?