Not sure what you mean - distance directly away from an observer correlates with time (things further away look younger due to the finite speed of light), but in general it's just a measure of distance. It's right there in the units - light (speed) years are m/s * s; that is, metres. I'm not aware that astronomers use ly as a unit of time, unless that's changed since I studied it for my undergrad, although that was admittedly some time ago.
I don't think it is so simple. As a rule of thumb, sure.
But space is supposed to have been expanding while the light was in transit, so 13 Gy-old light has travelled way more than 13G light-years, and the object that emitted it is "now" dizzyingly farther away even than that. (Scare quotes, because simultaneity is meaningless at such a distance; and it must be outside our light-cone, so can't really meaningfully be said to exist in our universe anymore.)
I am not clear at all on how light experiences expansion of space, as that seems to require time, and light travelling in vacuum doesn't experience time.
Light emitted only a billion years ago has traveled only a little more than a billion light years. But what's a few million light-years, extra, among friends?
Well you're touching on some deep and difficult stuff here. There are many others who understand and can explain all this better than I, but I'll do my best to comment usefully, however before I do - none of what you said here has any bearing on the original question of whether 'light years' are units of time. They're not. Anyway, all this stuff is fascinating, so here goes:
> But space is supposed to have been expanding while the light was in transit, so 13 Gy-old light has travelled way more than 13G light-years, and the object that emitted it is "now" dizzyingly farther away even than that. (Scare quotes, because simultaneity is meaningless at such a distance; and it must be outside our light-cone, so can't really meaningfully be said to exist in our universe anymore.)
Close but not exactly - the point where the light was emitted is now 13G light years away, because by definition, a light year is the distance light travels in a year. The object emitting that light, however, was accelerating away from us and "now", that is, following the expansion that occurred during the time the light was in transit, is more like 42G light years away. When the light was emitted, the object in question was much closer than that. The expansion of space has changed the definition of a metre and therefore effectively moved us and the object apart. A (crappy) visualisation of an object A emitting a photon P at point X towards an observer B (first, later, and now are of course in implied scare quotes):
first: AXP-B
later: A----X-P--B
now: A-----------X-------PB
The distance XB is the distance P has travelled in total, 13G light years in our earlier example.
> I am not clear at all on how light experiences expansion of space, as that seems to require time, and light travelling in vacuum doesn't experience time.
This is a great question and took some research for me to get close to being able to answer, but the best I can do here is to link some related discussions [0][1][2], and summarise that photons don't experience anything because they have no frame of reference, so it's meaningless to ask whether or not or how they experience time, or indeed anything else. Photons always move at C in every frame of reference (remember there is no such thing as an absolute velocity for an observer, it's always relative to a reference frame), so there can be no frame of reference comoving with a photon in which time can be measured (and indeed, in every reference frame, time appears to move at the normal rate - time dilation only occurs between two frames). What we see on Earth is that a photon is "stretched" by the expansion of space and therefore red shifted - and as I guess you know, that's a key marker astronomers use to calculate the distance a photon has travelled - more red shift means more distance. As very distant objects are accelerated out of our light cone, they are red-shifted so far that they eventually disappear - in fact, far far into the future, the same will be true of everything in the universe, meaning that any being looking up hundreds of billions of years from now will see no galaxies outside their own.
> Light emitted only a billion years ago has traveled only a little more than a billion light years. But what's a few million light-years, extra, among friends?
As explained above, not so. Light travels at one light year per year. Expanding space is changing the meaning of distance but not the speed of light.
While astronomers are obviously very much aware that light-years is a measure of distance, "seeing further away" is a stand-in for "seeing further back in time." New telescopes are rated by how much further away they can resolve in terms of light-years because that is a direct translation into how close to the Big Bang they can resolve.
What I'm saying is that it is extremely useful that being able to resolve objects 13.2 billion light-years away means being able to see back 13.2 billion years in time. The units are 1:1 convertible, and astronomers therefore frequently interchange them in casual conversation.
This might resolve my doubts that the phenomenon could be an artifact of different conditions in the early universe.