Thank you for posting to the community.
"Compatible with 4.4.1.0" means the agent is compatible with any Controller having version >= 4.4.1.0, so it shouldn't be a problem if the controller's version is greater than 4.4.1.0.
Could you please check the followings?
・Could you please check the Prerequisites for Object Instance Tracking again, especially the OS version?
From the Java supported environments, oracle jvm supports Solaris Sparc 64, Windows, Linux, so if you are using MacOS, Object Instance Tracking may not be available.
・Where did you get the warning about missing tools.jar or needing to use an Oracle JVM?
If it is a popup that appears after selecting ON on the Object Instance Tracking subtab, it always appears even if Object Instance Tracking is available.
Then, after selecting OK and get "Error Saving Items" message, there can be a permission issue, so please confirm that your role has "Configure Agent Properties" Edit Permission on the application.
・After enabling the Object Instance Tracking from the controller, could you please look at the agent log and see logs related to ObjectMonitoringService? If there is a log like "Object Instance Monitoring cannot be enabled on this platform," the platform may not be supported.
Best Regards,
Hiroki