Sorry, I am sure your plant is not S. pseudocapsicum. That plant never gets as large as your plant in question.
There are many edible Solanum, and it is likely yours is one of those.
There are chapters of the North American Fruit Explorers, all over Florida. Also California Rare Fruit Growers...
I'm sure it's not chickweed, which has opposite leaves.
It looks like a spurge; if so, it will bleed a milky sap when you break a stem. Try it, and report back.
One of the problems here is the common name thing. At least 7 species are called "pennywort". Which one do you mean?
I will concede I was not very sure of the Cymbalaria identification, and there are only two species of that genus that I know well.
I am sure it's not Umbillicus, which I do...
OK, the first two pics (the plant in question) is most definitely NOT Umbilicus. Nor is it Hydrocotle.
It is much more likely wall ivy - Cymbalaria. I would recommend you weed it out of your yard.
I notice between the plant in question, there are some chickweed seedlings - this is a good food -...
Carol, my first thought was of your drought - it makes the news even here. I would water the hibiscus generously every few days, and fertilize twice a month.