When we read that, for instance, M31 is 2.54 ± 0.11 Mly (778 ± 33 kpc) away from us, does this distance estimate take into account the travel time of the light we observe? In other words, what is the "timestamp" on the distance estimate? Does it actually reflect how far away M31 is now?
It represents the distance when light measured was emitted. That is the conventional way that the distance to anything is defined isn't it.
To do anything else requires a very accurate knowledge of what will happen to an object in its future. You could in principle do that, if you have very good measurements of an object's velocity and know all the forces acting upon it) but it doesn't make much difference unless something is travelling at a fair fraction of the speed of light (and M31 isn't).