What your state allows
Updated
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Two layers, two conversations
The federal layer says what an acidified food is and what is required of one. The state layer licenses your kitchen, inspects it, and decides whether you may sell what you make and where. Both apply, and a clear answer from one does not settle the other.
Cottage food usually does not cover this
Cottage food laws exist for products whose safety does not depend on a controlled process: baked goods, jams, some confectionery. An acidified sauce depends on exactly such a process, which is the reason it tends to sit outside those lists and the same reason it sits inside the federal regime. Some states carve out specific acidified products with a stated acidity requirement, so it is worth asking rather than assuming either way.
Describe the whole plan, including where you will sell
A farmers market, a retail shelf, a restaurant and mail order across a state line can each sit differently. A maker who asks only about making the product gets an answer that does not cover the venue they were counting on.
Write down who told you what
Name, date, what you described and what they said. Staff change and guidance gets restated, and being able to say who told you in March is a different position from remembering that somebody said it was fine.
Ask before the equipment, not after
The order that costs least is state first, process authority second, equipment third. Makers reverse it constantly, because buying a kettle feels like progress and a phone call does not, and then find the room they planned to use is not one they may sell from. The call is free and it is the only step that can invalidate the others.