The next_event attribute is defined by the contents of the schedule. Why would you expect to be able to override that? A schedule is AFAIK not meant to be updated programmatically, they can only be edited in the UI or through YAML (depending on how it was initially defined).
If you want to programmatically store and update a date, you should use an input_datetime helper rather than a schedule. Or if you need to keep track of multiple dates use a calendar integration.