'Owned by' field is set automatically once another custom attributes value changes

There are several ways of doing this - Attribute customization likely is not the best approach. It basically depends on what the real use case is to decide the approaches. A follow up action might be possible and, with limitation, a calculated value. See my problems with many similar requests below.

I personally think this is a broken process/use case and instead of such an automation a work item query used by the responsible person to assign the owner or pick up ownership in the project would be a lot better.

They could use the query to assign the work item (as RTC is designed for) and the automation is just pointless. A lot of the automation I have seen requested here is pointless, because it tries to automate a process at a point where the process was broken by the management and users. An automation that is so simple that it does not need a human to do it is typically showing the automation is pointless and not really needed. Rules that simple to put into logic usually don't provide any benefits.

 I believe you would have to write your own custom follow-up action to perform this.   You would need to decide where to store your Component->Owner mapping information, so that you can modify that information without modifying the source code of your follow-up action.   A couple of potential places are in the process-XML, or as a file attachment to the project area process.