Is there a well-known, accepted method to safeguard the private keys (such those for AWS or Stripe) in the project so they won't leak without permission?

Never store private keyes in your app. There are ways to hide/obfuscate the keys but there is always a way for attacker to access them. Also not kotlin but kotlin colored

can you suggest any tool or something?

Try hidden-secrets-gradle-plugin but again, nothing is secure when present in installation APK

can we use secret manager or vault such as Google secret manager or Hashicorp vault?