I did some digging in one of my favorite older resources when it comes to plant lore and legends. Funnily enough, it’s actually called Plant Lore & Legends! Here are a few quotes from that book - it’s available for free on Project Gutenberg - and my interpretation of them for magical correspondences.
It is strange to say how much this tree was sought after by the credulous; and though not an uncommon Walnut, Queen Anne, King James, and many of the nobility of the realm, even when the times of monkish superstition had ceased, gave large sums of money for small cuttings from the original.
→ This makes me think that walnut is tied to wealth, abundance, and rarity.
The belief that certain trees are haunted by the Devil, or by malignant demons who act as his satellites, is of world-wide extent, and, in connection with tree spirits, the subject has been incidentally touched upon in the previous chapter. A Russian proverb says that “From all old trees proceeds either an owl or a Devil;” and in many countries where a tree becomes old and past bearing, its sterility is attributed to a demon. The Albanians believe that trees are haunted by Devils which they call aërico . Certain trees are especially affected by these aerial demons: these are the Fig, the Walnut, the wild Plum, the Mulberry, the Sycamore, the Pimpernel, the Willow, and in general all fruit trees (but especially the Cherry) when they are old and cease to bear.
→ Walnut trees, when done bearing fruit, are said to be more prone to spirit inhabitation. This leads me to connect old walnut trees to be closer associated with the Otherworld and spirits.
The Walnut-tree, of which it is said that the shadow brings death, is in some countries considered a funeral tree.
→ This quote here ties the walnut tree directly to death and they dying.
There are so many instances of walnut being mentioned in this book. You can take a look for yourself here → https://www.gutenberg.org/cache/epub/44638/pg44638-images.html ← if you’d like to look more!