I think it would be useful to come up with an easy to find definition of "captive/cultivated" on the iNaturalist site (there may already be one there, but if so, it is hard to find). The cultivated issue represents a gradient, but it can be useful to define portions of that gradient for grouping. Since we only have the extremes (wild/cultivated) defined for now, we should probably work off that.
The main distinction between "captive/cultivated" and "native/naturalized" can be summed up in the terms spontaneous and deliberate. Spontaneous individuals are those that got where they are without human help. Deliberate individuals arrived with human help.
As a definition for cultivated plants, I think the following works well:
A plant is cultivated if it was intentionally planted by a human in a certain space (e.g., garden bed). An organism is no longer cultivated if it is at least two generations removed from the place it was planted or two generations from the planted individual(s) if the space has "reverted" back to natural conditions (i.e., 2 generations removed from being tended).
The reason for 2 generations is that it is easy to get waifs which don't persist. 2 generations is just a bit more robust in excluding plants that just barely qualify as spontaneous and can't really make it in the wild on their own.
How to determine if a plant is 2 generations removed from a planted plant? I would say if there are numerous plants outside a garden bed and they are fruiting, then I can be pretty sure that the plant is outside the bounds of cultivation. There will always be a gray area and a gap in one's knowledge about the plants in the area unless that person planted the original plant, but I think this is a pretty good start. If need be, we can incorporate this into the definition.