The subject can be confusing when you first encounter it. I agree with
@phinds that you need to be careful and make sure you understand what precisely is meant by each statement you use.
You started well enough with defining observable universe. But further down the post it gets a bit murkier.
Let's go over each content-bearing statement.
The most distant would be the cosmic microwave background radiation. That's just the most distant galaxy, whereas there is quite a bit of space seen further away, at the time when galaxies hadn't yet formed (but filled with gas). However, it's beside the more important point addressed below.
Here we have a citation of distance, but no indication what distance is being used. There is a
whole lot of different distance measures used in cosmology, where their use is dictated by certain measurable properties, but doesn't necessarily resemble anything like the everyday meaning of distance.
In particular, the distance cited above is 'light travel time distance'. It is what you get if you multiply the time it took light to arrive to us to be observed times the speed of light. This would give you something very much like the everyday notion of distance, if not for the fact that we don't live in a static universe.
If you imagine an emitter at some initial distance ##D_{initial}## from the observer, sending a light signal in a universe that is
not undergoing expansion, then by the time ##t## the signal arrives, it will have traveled ##D_{travel}=ct##. The object at the moment of reception is at distance ##D_{final}##. Because the universe is static, all distances are equal: ##D_{initial}=D_{travel}=D_{final}##.
But, if the space, through which the light signal is travelling, is expanding, these distances will differ. After emission at ##D_{initial}##, the signal begins to approach the observer, while the emitter is receding from its initial spot. After time ##t=D_{travel}/c## it arrives. By that time, the emitter has managed to recede to ##D_{final}##. Now, ##D_{initial}<D_{travel}<D_{final}##.
So, if asked what is the distance to the observed object, we can say it is either of the distances, and each will have a different numerical value, but also mean different things. ##D_{initial}## is where it was at emission, ##D_{final}## is where it is now (in the sense that, if you could stop the expansion and take a measuring stick, that's where you'd find it). The distance ##D_{travel}## doesn't have any concrete physical meaning that'd map to our everyday understanding. The emitter neither was nor is at that distance.
So, after this long-winded exposition, the point would be that one should not use the light travel time distance as a measure of the size of the observable universe, because it's essentially meaningless, if convenient in some scientific contexts.
It's also, perhaps, important to note that the light travel distance is not a direct observable - you can't ask a photon how long it's been going for. Neither are any other of the distances. The main direct observable is the redshift, with all distances derived with the use of cosmological models. So, providing you do want to make a statement on the size of the observable universe, you do have to settle on a derived value.Now, what do you mean by that, exactly? Is this the high estimate for the light travel time distance? Using Hubble what? The HST? That's used for all cosmological observations, together with other instruments. The error bars on the age of the universe (so, also the light travel time distance) are not reaching the 15 Gyr mark.
Or, do you mean Hubble law? Since you can arrive at a number resembling in meaning the age of the universe, that close to 15 Gyr (14.5-ish) using its inverse and a lower estimate for the Hubble constant. That'd be a whole new kettle of fish, however, since again, there's no sense in which the farthest observable objects are at 15 Glyr, nor is the universe in any sense 15 Gyr old.That's precisely the meaning of the reported size. As explained earlier, it's the ##D_{final}## distance.
Now, you could argue, that you'd rather use the ##D_{initial}##, in which case the universe would be some 88
million light years across. But that seems even more conceptually problematic, as I think you'd agree. The ##D_{travel}## has no physical meaning, and as such is the worst measure to use.
Whereas ##D_{final}## does map, at least partially, to what we mean by where something is. In particular, you can modify the question, and instead of 'how far is the object I see after time ##t## since emission' you can ask: 'how far did my signal travel to after time ##t## since emission' - which is the same number.
And finally, ##D_{final}## has a technical meaning that maps onto the definition of observability - it's the spatial extent of the base of the observer's light cone, as drawn in an expanding space = the size of the causal patch around the observer.
