You can use release variables to do this. Feel free to reachout if you need any assistance.

https://docs.microsoft.com/en-us/azure/devops/pipelines/process/variables?view=azure-devops&tabs=yaml%2Cbatch

https://docs.microsoft.com/en-us/azure/devops/pipelines/release/?view=azure-devops#how-do-i-specify-variables-i-want-to-edit-when-a-release-is-created

The problem occurs when I want to deploy the same API to other environments like QA/UAT/Prod. Since each environment is having separate databases

For this issue , there are several ways to achieve this. You can add Replace Tokens extension to the job to replace the database connection string in appsettings.json.

You can define your variable like below:

{
  "ConnectionStrings": {
    "DefaultConnection": "#{connectstring}#"
  }
}

You can refer to this case and lab for details.

Here are some reference for the same issue:

Replacing database connection strings in the Docker image

Set Json Property task to replace the ConnectionStrings