When I quit mail, then reopen, it can synch now. But for the last several days, it wasn't synching even when I closed it and reopened. I had the same situation with the iCloud email, which I don't use for sending mail but do receive Apple News in. I clean it daily from my phone or from the MacBook. The not synching has been a one way deal. If I delete mail on the MacBook, it deletes on the phone automatically. But it hasn't been working in the opposite direction: deleting on the phone has not been deleting from the MacBook. For the last few minutes, it has been operating more normally on the MacBook.
Thank you for your help. Maybe the problem has resolved.