They get a little morning sun, which is then blocked by the oak tree (which may be coming down in the fall) Yesterday, I kept track of how much direct sunlight they get, and was dismayed when I saw that they were in the shade again by 5:45 - which means they receive barely six hours.
In the afternoon, this part of the vegetable garden is shaded by 2 pine trees. Those pine trees are also coming down in the fall!
Someone wrote a comment that bright shade also benefits the plants, and I'm pretty sure my tomato plants are getting plenty of that. After all, the rest of the vegetable garden gets about eleven hours of direct sun.
Thankfully, I planted a bunch of leftover tomato plants in containers yesterday. They are sitting safely in the pool area, and get the same 10-plus hours that the other vegetables get.
I have started to notice that most of the tomato plants - although planted in the least sunny spot, have lots of flowers on them, and look like they will soon set fruit. So maybe everything will work out!