technically anything that grows a cash crop is a plantation. If a sugar cane plantation had collective ownership it be a plantation co-op. Just like how it would be a farm co-op if it grew veggies.

The weird part is avoiding ownership and work. "we lived on a sugar can plantation" versus "we lived on our sugarcane plantation." Her talking about the quaint idyllic life of harvesting sugarcane ignoring the, potentially, hundreds of slaves that were actually doing the harvesting, also strange and weird and sus.