Archaeologica.org

https://www.heritagedaily.com/2019/03/r ... nds/122933

Archaeologists with the University of Cincinnati used the latest technology to find evidence suggesting ancient Maya people grew surplus crops to support an active trade with neighbors up and down the Yucatan Peninsula.

There is concordable discussion on who, where, when, and why agriculture was first used
In my mind the why was simple.
Food.
Gardening was, and still is, a common way to feed a family.
But what do you call agriculture that produces more than you can eat? (Or even produces non-eatable stuff?)
I think it then becomes farming.
The on purpose growing of more than you can personally use for trade purposes.

It would appear these were farmers, not gardeners.

Quite so. During the H/G phase it is not hard to imagine someone coming across a stand of wild grasses and deciding that the seeds had possibilities. From there the idea that those grasses could be controlled does not seem at all far-fetched ( "doing a bit of gardening") as you say. I'll even buy your distinction between gardening and farming as the former implies a part-time aspect while the latter does not.

Israel Finkelstein, with his theory of pastoral nomads settling down at the beginning of the Iron Age to eventually become the Israelites, Moabites and Edomites, puts the cause of that change to the Sea People attacks which destroyed the coastal agricultural states that traded grain to the nomads for meat and skins. Lacking that source of grain they had to start growing their own.