The two quotes from the TMoST cited above are not mutually exclusive.
Of the four facilities listed, the first one;
"large recreation area" -is the one referred to by this quote...
"Although this recreation area has never been shown in any past episodes, this set has now been built and will be seen in the third season."
This is the set we've been calling the herbarium, so it
was built, and it
was seen in the third season, so TMoST is correct.
The fourth one;
"exotic entertainment center" -is the one referred to by this quote...
"Therefore we intend to build a simulated "outdoor" recreation area which gives a realistic feeling of sky, breezes, plants, fountains, and so fourth."
This set was obviously never built, and we therefore never saw it, but then the TMoST doesn't claim otherwise, only that they
intend to build it, so again TMoST is correct.
As for whether the Herbarium was a standing set, I still say it was. I worked in the theater business building sets, so I’m very well aware of how sets are used and stored; and being an original TOS fan since the Sixties, I’ve certainly been around long enough to know how the Trek production handled their set requirements. So unless I see an original memo or an interview that says otherwise, I’ll remain unconvinced that it was anything other than a permanent addition to the other standing sets, as was the case with the auxiliary control room and emergency manual monitor.