The original question seems to be pretty much covered: TMoST
In in-universe terms, the idea of "botany lab" being part of an accessible recreation area makes plenty of sense. Naturally, there would have to be quarantine areas for the nastier sorts of flora encountered in the TOS adventures, but consistency is well served by assuming that everything from "Man Trap" to "ITITNB" involves the same overall facility, for the reasons already given by mickemoose
However, I've always been a bit uncomfortable with the idea of a starship moving a bunch of trees around. They don't uproot entire tribes and put them in onboard concentration camps in order to study languages; why haul timber for study purposes? And surely "recreation" could be arranged by other, more practicable means as well. In that sense, it would be nice to think of the "Man Trap" lab as a compact science-dedicated facility, and the seeming arboretum as a simulation that actually takes up very little room and can be stricken down so that the same room is available for other purposes at other times.
Remember those four mysterious glowing squares on the dorsal surface of the saucer rim? Or, even more interestingly, the three glowing squares, with one asymmetrically remaining dark? These could be stargazing rooms available for a variety of purposes (as suggested by the variety in the lighting status), and our heroes could have set up a park-lookalike in one for "season three" of their long and tedious mission...