AWS Secrets Manager is a perfect choice if you're launching your start-up or have small number of secrets to manage but tight regulations - PCI DSS, HYTRUST, ISO 27001 and others.
Hashicorp can be wiser choice if you need multi-cloud or hybrid cloud options or will need to manage thousands of secrets.
Each option solves a secrets management problem but bring a new problem - you'd have to implement and maintain it. If you consider getting help with this - check out our DevSecOps as a Service
If you are not ready to consider the implementation of a tool - you can check out our Kubernetes Penetration Testing Service.