The following is not an answer; it's a comment.
Also, I'm not providing historical information.
However, I feel that the information that I present is interesting and useful to know.
Thinking that a catenary arch has general usefulness in architecture is actually problematic, I will argue. There is a wrong assumption at play.
A catenary is the mathematical solution to the problem of a structure (either hanging chain or standing arch) that has a uniform weight per unit of length. As we know, the catenary is the solution with equilibrium everywhere along the length.
However, in the case of any large building you make the walls thick at the base, so they can carry the total load, and you make the walls thinner as you go higher. That means that near the base the structure will have more weight per unit of arch length than the top section. And that means the mathematical solution will be somewhat different from a catenary.
With domes using a catenary cross-section is even less applicable.
First, take the case of a theoretical dome, a dome with a shell that has the same thickness everywhere. What can we say about its equilibrium shape? If you would take a catenary arch, and you would rotate that around its symmetry axis then the resulting dome that is not an equilibrium shape.
Imagine two catenary arches, at right angles to each other, crossing each other at the top. That means the top stone is shared between the two arches. It follows that that in order to be overall in equilibrum the cross-section of that structure must be somewhat flatter than a catenary. Imagine adding more and more crossing arches (adding up to a dome). At the base of that structure weight will be contributed by each arch, but at the top most of the weight will be shared weight.
So: even in the case of a dome with a uniform thickness of the shell the equilibrium shape will not be one that has a catenary-shape cross section.
Let's take one of the most famous domes: the Pantheon in Rome. Naturally the builders of that structure constructed it with a tapered thickness of the shell. Very thick at the base, gradually thinning out towards the top. (Also, the aggregate in the concrete varies, with pumice used at the very top.) The result: different weight per unit of surface from base to top.
So, in the case of a real world dome there are two independent factors that affect what the equilibrium shape will be, and both of them will shift the mathematical solution away from a catenary cross-section.
Of course, this doesn't necessarily mean that you cannot build a dome with a catenary-shape cross-section. If the structure is strong enough then you can. The structure has to be able to withstand wind loads anyway. That is, the structure must be able to withstand bending stresses anyway, so chances are that the bending stresses that arise from not being an equilibrium shape are well within the range of what the structure is able to handle.