First I ran
select * from ExecutionLog3 order by TimeStart DESC
This gave me a list of events that I matched with the scheduled times of the jobs:
So I went to the portal and checked the dataset. Turns out caching was enabled:
The @schedule_id parameter on sp_update_schedule does refer to the schedule_id column on msdb.dbo.sysschedules
sp_update_schedule contains a call to sp_verify_schedule_identifiers to validate the schedule, and it's from this verification step that you are getting that error (message 14262).
EXECUTE @retval = msdb.dbo.sp_verify_schedule_identifiers