Encryption and decryption of Request and response for REST API
In case you want to use AWS KMS without the raised issues, you can use AnonyFlow API for encryption/decryption. it is using the AWS KMS in the background and manage the private keys for you in order to avoid the keys issues you have raised, therefore you enjoy the service without worries.
It's very easy to consume the api, you can use the anony-value for encrypting one or more string values (string array) or use the anony-packet for encrypting json data - you can even define specific keys in order not to encrypt the entire json.
the best practice would be to consume it in your server side code. you can even create a serverless service on aws or any other platform to handle it.
Disclosure: I'm part of AnonyFlow creators.