If mouse gestures or keyboard input doesn't go through to your Mac, try these steps:
Make sure that Observe > Control is enabled in the Remote Management settings.
If that is already the case, try to uncheck and recheck both options or disable Remote Management and enable Screen Sharing instead*. Then, try to connect. If you are able to control your Mac, try to re-enable Remote Management. Some users have reported that switching between the services solves the issue.
* This operation should be performed while you have physical access to your Mac or you may lose access and not able to reconnect.
Make sure that Observe mode isn't selected in Screens. Control mode should be enabled in order to send mouse and keyboard commands.
Screens for iOS: Select the cursor control mode that is the most appropriate for you. Some users set Screens in Touch mode while they want to control their remote Mac like a trackpad. In those cases, you should enable Trackpad mode instead. You'll find more information in the Cursor Control Modes article.
Multiple Displays on the remote Mac?
If there are multiple displays attached to the Mac you're connecting to, there is a known bug on macOS that may prevent the cursor from moving. Please check out this blog post for more details and workarounds.