My QuickSight cannot connect to RDS PostgreSQL DB via VPC

It looks like there is network access but access is being stopped by postgreSQL. To debug this, add this line in pg_hba.conf:

host    all             all           all            md5

and restart posgreSQL (or reload configuration).

Then check again to see if QuickSight is now allowed to access your instance. If it works you may want to look into hardening that pg_hba.conf line there to restrict access to just QuickSight.