Server screenshot shows lock screen even when server is not in lockscreen

Are you saying that you're logged into your EC2 instance, I'm assuming Windows based on RDP, but when you grab a screenshot it's showing the lock screen instead of your active user session? If so, that's the expected behavior. The GetConsoleScreenshot API call is similar to the legacy KVM (Keyboard, Video, Mouse) days when you would connect a monitor to the back of your physical server and even if several users are logged into it, you would be presented with the login screen instead of seeing what active users are doing. The Console Screenshot service isn't using your credentials so it's not seeing your session.

I'm unsure what type of task you're trying to monitor on your instance, but something like CloudWatch Application Monitoring gives you the ability to setup Synthetic Canaries (configurable scripts) that run on a schedule, to monitor your endpoints and APIs. There's also CloudWatch RUM that can gather telemetry data on the performance and reliability of your application, including page load time, client-side errors, and user behavior.