Are there any state or county specific limits on how much powder or how many primers somebody can have? Or any special requirements on storage?

I believe that you have to search the fire code versus city ordinances.

Preferably in wooden cabinets or similar. Something that cannot hold pressure. You don't want it to become a giant bomb if there's a fire.

From the BATFE:

Smokeless powders designed for use in small arms ammunition are exempt from
regulation under 18 U.S.C. Chapter 40 and the regulations in 27 CFR Part 555.
Packaging that readily identifies the smokeless powder as being designed for use
in small arms ammunition may help in determining whether it is entitled to the
exemption.

https://www.atf.gov/explosives/qa/smokeless-powder-designed-use-small-arms-ammunition-subject-explosives-storage

Also, for purposes of classification, smokeless powder used for small arms ammo is not considered an explosive material:

Smokeless powders designed for use in small arms ammunition are exempt from
regulation under 18 U.S.C. Chapter 40 and the regulations in 27 CFR Part 555.
Packaging that readily identifies the smokeless powder as being designed for use
in small arms ammunition may help in determining whether it is entitled to the
exemption.

https://www.atf.gov/explosives/qa/smokeless-powder-designed-use-small-arms-ammunition-subject-explosives-storage

Informative SAAMI video on storing smokeless powder.  it does not include black powder.

Tests conducted by placing smokeless powder in a large bonfire resulted in no negative effects.  Smokeless powder is therefore not considered a hinderance to firefighting or other emergency response situations.

Starting at the summary at the video's end...


What Happens When Smokeless Gunpowder Burns?


https://youtu.be/Vt6LGcn4I_4?t=18m48s

See pages 5 & 6:

https://www.alliantpowder.com/resources/catalog/AP399_2023AlliantPowderReloadersGuide_SinglePgsNoCrops.pdf

Not aware of limits for regular personal use and typical amounts aren't a hazard unless you place large amounts in a sealed container like a safe or have it in a condo.

Now if you're talking excessive amounts like 500lbs of powder and 1000 bricks of primers, then that could be dangerous.