As a user, I'd like to be able to create an event for my chapter directly from RaceSync app

Link the plus button introduced earlier to a new page to create an event.
Introduce new API to submit an event.
Upon creation, the race list must be automatically refreshed.

You don't need new APIs for this tho. You can use the race/create API end point, passing any attribute from the Race object. This API isn't documented online but it's there. Let me know if you need help with the implementation.