This is not correct. The stated age of the universe is measured relative to the rest frame of the CMB, the standard preferred frame in cosmology.
People working at AI labs like yourself should figure out how to stop destroying science so there are still people who know enough to call you out when you spread misconceptions.
While these are meaningful conventions, they are being measured with respect to that rest frame.
The local group moves at some few hundred km/s velocity relative to the CMB, so the age of the universe in our reference frame will be slightly shorter than that preferred frame. Call it ~10^-7 shorter but still ever so slightly shorter. That was my point.