What is the ruling on conveying information to the manager that so-and-so was present but did not sign the attendance sheet, and what is the solution for that?

If a person is responsible for monitoring employee attendance, or is assigned this by the manager, then there is no harm in his work. This is not the prohibited backbiting (namimah), but rather a beneficial reporting, similar to the man who informed Musa (peace be upon him). However, if backbiting is devoid of such benefits, then it is prohibited. This ailment is treated by reminding the backbiter of Allah and by avoiding him.