Hi Emily,
Could you advice if I need to reschedule this background job again or just wait for next schedule running?
Here no need to reschedule the same job again,you could wait for next schedule running.Or if still you want to update stats try to run it through br*tools at OS level for once.
Any affect on database table update?
As you're also aware about why we need to update stats for the database,as it's completely related with the performance of your Database.So in my opinion if you feels performance is not up to the mark than you can go for it manually for the day.
Good Luck ,
Gaurav