Thanks Rukbat for the reply. You can choose what apps can still use the mobile data.
I'm not worried about the amount of data used actually, but the duration of the battery. 1/2 without the data saver on, over a day with data saver on.
It is my main account. I removed the other gmail account that was installed. By the way, I had the same issue with that second account after reinstall.
Right now, only that account is in the phone.
Thanks B. for your help.