I find myself inclined to speculate on the workings of agriculture among the High Elves of Middle Earth leading up to the time of the War of the Rings* - and from information within The Lord of the Rings.
We are told enough about the agriculture and gardening among Men and Hobbits to understand how they sustain themselves, but very little indeed about the Elves. We hear nothing of fields and farms, or agricultural labour, of the kind that would be needed to sustain Men and Hobbits.
Elves are said to enjoy hunting, arts and crafts, singing and scholarship; but the idea of a Elf engaging in ploughing, herding cattle, shearing sheep and other agricultural tasks seems almost absurd.
Indeed, it seems as if the Elves of Rivendell and Lothlorien must support themselves "by magic" - and what slender evidence there is, suggests that this might be so - in a way.
In The Lord of the Rings, there are only three colonies of High Elves in Middle Earth: Rivendell ruled by Elrond, and Lothlorien ruled by Celeborn and Galadriel Of these we are told a fair amount. Of the third enclave, the Grey Havens ruled by Cirdan, we know almost nothing.
The problem is that it is made clear the Elves of Rivendell and Lothlorien have almost-nothing to do with the Men (or Hobbits) in their vicinity.
There is near zero communication between these Elves and the agriculture-pracicing Men (and Hobbits) living nearby; which apparently rules out any significant amount of these Elves trading for food.
Yet, there are certainly feasts at the rather small and exclusive enclave of Rivendell (population a few hundreds, at most) - and there are plenty of other good like clothes, and the materials for craftsmanship in several areas.
Lothlorien supports an apparently larger population, of what seem like thousands (from the description of their tree city, and implied by their role in the War of the Ring); Lothlorien Elves also weave cloth, make ropes, have tools and weapons in plenty; and access to supplies of the cereal grain that goes-into Lembas.
Lothlorien provides a clue to part of a possible answer in the form of Galadriel's gift to Sam: the little box containing a marvellous kind of earth; even a single grain of which is capable of causing massively accelerated and healthy thriving of plants - such that several/many years of growth happen in just one season.
This must be magic, not biology; and that points at Galadriel's Elf ring - one of The Three - as a possible basis for this magic.
I am therefore inclined to speculate that the Elves of Lothlorien were capable, by using the same kind of magic that enchanted Sam's gift, to grow what they needed very quickly, with little effort, and using only small areas of land.
So, there is indeed "High Elven Agriculture" - but it is highly and rapidly productive on such a small and temporary scale as to be almost unnoticeable to the casual and short term visitor.
If this can be allowed; then we have the same answer for Rivendell, where Elrond wields another of the Three Rings, and indeed the senior and most powerful of them.
As for the High Elven enclave of the Grey Havens, we know that its ruler Cirdan originally had the other Elf ring, but yielded it to Gandalf (who puts it to altogether different uses). There must be sufficient elven mariners and shipbuilders in the Grey Havens to fulfil its primary role - a few hundred, perhaps? - and these will need feeding and provisions.
But we also know that there is a frequent movement of High Elves between the Grey Havens and Rivendell.
So, in terms of its agricultural "means of support" - how it feeds and clothes itself - the Grey Havens, may well be an outpost of Rivendell, and so a beneficiary of the magical agriculture sustained by Elrond's Elf Ring.
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*I leave aside the Wood Elves of Mirkwood - because they are only much known via the Hobbit; and before the habitations of Middle Earth had been defined by the later book. From what we are told in The Hobbit, the Wood Elves live by hunting and trading (for instance for wine and food) with the Men of Lake town; and - it is vaguely implied - with other more distant but undefined Men.
What the Wood Elves are trading for their food and wine is unclear; although it may be that the large treasury of the Elvenking (gold, silver, jewels etc) is being gradually expended as a capital resource. If the Mirkwood Elves do depend on Lake Town, it provides a self-interested motivation for the Elvenking's crucial assistance in saving the residual population, and rebuilding Lake Town after Smaug's depredations.
I also tried to focus here, only on what is gathered or guessed from a reading of Lord of the Rings as such - therefore ignoring any things JRRT said about Middle Earth; and also ignoring the posthumously published material of a History of Middle Earth nature.
