questions about the reincarnation of Baron Harkonnen in the Dune saga would be entirely on topic
Was there actually a reincarnation (as opposed to a ghola) of Baron Harkonnen in any of the Dune books?
The genetic memory of the Baron overwhelmed and corrupted Alia, as her in utero exposure to the Waters of Life opened her genetic memory before she had learned enough Bene Gesserit training to protect herself adequately.
I wouldn't call this an actual reincarnation, but there are parallels in the concept, as the personality of the Baron became increasingly dominant.
I didn't read the Dune books by Frank's child, but in the original 6 Dune book saga, the Baron was never reincarnated. His influence corrupted Alia, but that's the extent of him being reincarnated.
According to Wikipedia, there was a Baron ghola, but your question specifically excludes gholas.
What do you mean by "reincarnation as opposed to a ghola"? In the Dune universe there is the "other memory" of the Bene Gesserit, and there are gholas
whose memories can be restored under some extreme circumstances (which IMHO makes no sense scientifically).
I would say a ghola is the closest thing to reincarnation in the Dune universe.
And yes, there is a ghola of the Baron in the Hunters of Dune by Brian Herbert, not in any of the original books by Frank Herbert.