Oh dear. This is one situation where the stuff that exists on-line is extremely misleading indeed, I'm afraid. We are going to be doing "garden and landscape" om L&T in October when I hope we can iron out a few of these things. For now, however:

The "wood, grass and water" of Launcelot Brown and co was the "park". Chapter 42 says that Marinne was not in a park, but in the pleasure-grounds- i.e. in the gardens themselves."Park " is distinct from both "pleasure-grounds " and "garden", in JA.

Garden designs were far more individual than some websites would have you believe, and there were several garden "types" that were very popular at the same time. What is actualy quite important is that the "great gardens" of the aristocrats were not necessarily copied by the gentry, who had different requirements as to land usage.

Some dates- Capability Brown died about 1783, and his "style" was continues by several others, notably Eames and Repton.
The Picturesque style became popular after 1790, and had more or less petered out by 1810.Repton did adopt the picturesque style himself, but modified it greatly.

Grecian temples are not part of Brown's style; he only included them when the customer insisted upon it.The Grecian temple has as special symbolic significance in 18th century gardening, that has to do with lasting goodness and universality. I think Marianne wandering in a Grecian temple is a sign that she thinks of herself as heroically tragic. The fact that the Palmers have one puts them squarely with the gentry, not the aristocracy. The "wildness" at the extremities of the garden was a classic Picturesque/Reptonian touch, but Brown did it as well.