Or, if a seller of a wholly owned property is a partner in an LLC that is a buyer, can that purchased property be their 1031 replacement property?

Which ignores that the purchasing LLC is a different entity than the seller. A partnership LLC is not a disregarded entity. Even if the seller had a single-member LLC, it's still not the same owner of the property. Just because it looks like LLC-to-LLC with the same member in each LLC. Is that where you're confused?