Adding the link to the manual of how to implement Logging to Special:Log on an extension:
https://www.mediawiki.org/wiki/Manual:Logging_to_Special:Log

We would need answers to the following questions to determine the complexity of this task, or in general to actually implement it:

• Name of the log (first selector on Special:Log)
  • I would suggest using a generic name here, and then having subtypes, see T321018#8334107.
• Who should be able to view this log? Should be public unless there are good reasons against it.

However, what happens if user disables registration via MyEvents on one wiki but the event is on another wiki? Ideally, the behavior should be that the disabling is logged on the wiki where the event page lives

It's logged on the "other" wiki. We can add this to the list of cons of a central DB...

Yes, I think the log should be public.

I'm trying to learn more about how logs are structured/named. Would the expected hierarchy be that we have a general category (like event registration) with actions to monitor (such as enable, disable, restore, participant registers, etc)? For example, I see the deletion log lets you filter by type of deletion.

Do we need approval from anyone to add a new log type to Special:Log?