>How many cubic feet of soil, at what depth, do I need in order to stop purchasing food plants from the store, year-round?

Nobody can provide that evaluation for you without quite a bit more data. Your latitude will make a huge difference to the answer. Your altitude will make quite a bit of difference to the answer. The amount of available water will make a large difference to the answer. Those 3 alone (and notice that none of them are equivalent to "climate" though they all play a role in determining that) mean that the answers will vary across a huge range. There's also the nature of the soil in question, another far from trivial issue.

You can get some answers, however, from "How to Grow More Vegetables Than You Ever Thought Possible on Less Land Than You Can Imagine" by John Jeavons. Some of the answers can be very encouraging, some not so much. I did a weekend course with Jeavons a couple of decades ago in which he pointed out that a typical single olive tree will not even produce 1 cup of olive oil. The scale on which humanity now produces food is sometimes hard to imagine.