The state-by-state answer
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The state research that dominates a food business is a much smaller exercise here, with one significant exception.
Why this is a short list
Dietary supplements are regulated federally: DSHEA defines the category, 21 CFR 111 governs manufacturing, and 21 CFR 101.36 governs the panel. None of that varies by state.
There is no patchwork of exemptions to research because there are no exemptions.
Three questions
One: does my state require a license or registration to manufacture dietary supplements, separate from a general business license.
Two: may that manufacturing happen at a residential address under local zoning and occupancy rules.
Three: does my state impose any ingredient restriction or warning requirement of its own.
California is the exception
Proposition 65 requires warnings for listed substances above defined thresholds, and lead and other heavy metals occur naturally in botanical and mineral ingredients at levels that can trigger it.
This is not a hypothetical for supplements. It is a live and frequently litigated area, and it applies to anything sold into California, which for an online brand means everything.
The practical response: know your heavy metal numbers per lot rather than assuming, and take advice on where they sit relative to the thresholds.
Where to look
Your state department of agriculture or public health for licensing, your local authority for zoning, and FDA directly for everything substantive.
The federal material is well documented and stable. The state and local layer is the part that gets answered verbally in a phone call and then forgotten, so get it in writing.