Scientists still define astronomical time in years, with some recent refinements.
Q. Do scientists actually speak of the age of the universe in years, or do they use some measurement that does not refer to the orbit of one tiny planet?
A. Old habits die hard. The unit of time recognized by astronomers is an advanced refinement of what was originally another Earth-centric unit, the length of the day.
The International Astronomical Union, based in Paris, decided in 1976 to define the astronomical unit of time as one day of 86,400 seconds. The definition has been updated in later years and is not tied now to the actual variable speed of the Earth’s rotation.
(The second itself is now defined by the International System of Units as the duration of 9,192,631,770 cycles of certain structural change in the stable isotope cesium 133.)
The I.A.U. does define a year as well: 365.25 days or 31.5576 million seconds, unless otherwise specified.