In response to some of the complaints about Aurora PostgreSQL in this thread:

Aurora PostgreSQL Serverless should be considered a different product with different performance characteristics. We've been experimenting with Aurora PostgreSQL and have encountered the same memory issues mentioned here and elsewhere. It's impossible to autoscale read replicas based on memory usage, and there's no swap for temporary spikes. We haven't yet seen those problems with Aurora PostgreSQL Serverless. There is swap, which handles spikes, and whatever automatic scaling Amazon has implemented adequately deals with increased memory usage (if you're okay with a few terminated connections). I can't comment on the index-related issues, but I do suggest considering this product separately from Aurora PostgreSQL.