Ok I just noticed that when task is assigned to a group then it displays a small "i" icon besides workflow's internal status (as shown in first screenshot above) and clicking on that icon displays this message:
Retrying last request. Next attempt scheduled in less than one minute. Details of last request: HTTP Unauthorized to https://mysharepoint/sites/mysite/_api/sp.utilities.utility.SendEmail Correlation Id: b9a1cab8-319e-09da-a6a2-fa30cc3756cf Instance Id: 775169b4-362c-44e8-bc8c-b893474fde7a
Access denied. You do not have permission to perform this action or access this resource.
This seems like email sending issue (I have confirmed that email is not being sent probably due to SMTP issue) but this shouldn't affect the workflow right!? I mean task should still be approved/rejected?