Cottage food, and why pickles are usually outside it
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What cottage food is for
These laws exist to let low-risk products reach a market without a licensed facility, and the lists are built around products whose safety does not depend on a controlled process: baked goods, jams and jellies, some confectionery. The common thread is that the product is forgiving.
An acidified food is not forgiving. Its safety rests on a process and a measured result, which is exactly the thing cottage food law is designed to avoid having to supervise. So it tends to sit outside, and the same logic that excludes it from cottage food is the logic that put it inside the federal regime in the first place.
The jam comparison, again
A jam maker and a pickle maker standing in the same kitchen are in different regulatory positions. The jam is named in the exclusion list of the acidified foods definition and it is typically named on a cottage food list. The pickle is the example the regime was written around and is typically not. Same kitchen, same scale, different business.
Refrigerated ferments complicate it further
A live refrigerated product is not shelf stable, which changes the question again rather than simplifying it. Cottage food lists are generally about shelf-stable goods, so a refrigerated ferment is often outside on a second ground.
The lists differ by state
What is on the list, and whether there is an exception for pickled products, varies. That is a question for your state rather than for this page, and it is one worth asking in writing.
Some states do carve out specific pickled products, usually ones with a stated acidity requirement, so "pickles are excluded" is a reliable starting assumption rather than a universal rule. The thing not to do is infer your own position from a maker in another state, which is the most common way this gets decided wrongly and the easiest to avoid.