I think you are likely mistaking wax for oil.
Plants generally have a protective wax layer on their surface, just like humans have sebum on their skin. There are also other nonpolar substances within plant cells that would have a waxy or oily texture when clumped together, but they are less likely to be the cause, because they are not, in fact, clumped together, but exist as a single molecule here, another one there.
the seeds from the eggplants and tomatoes will emit oil when boiled
This is highly unlikely. First, tomatoes and eggplants are not an oil crop, and their seeds contain very little oil, when compared to other seeds such as walnut or sunflower seeds. Second, boiling doesn't really get oil out of an oil-containing seed in any appreciable amount.
And third, if there is anything in your soup emitting actual oil, you wouldn't end up with the water feeling oily. Oils are way too light, and boiling disperses them into an emulsion. You can easily observe this when you start a regular soup. Sweat some onions in oil, then add water and let it boil up. The water will be cloudy, but it won't feel oily to the touch, even though there obviously is oil in the mixture. The oil droplets at these small amounts of fat are just too small to coalesce into anything that makes your soup feel oily.
In contrast, plant waxes are much heavier and like clumping into a skin on the surface. So when you touch the water there, you can easily perceive it as oily.