Photo #1 shows the broad view of the top of the snag, with what looks like an acorn wedged in the hollow (smooth rounded bit that looks like a finger-tip). Note the green sheen of the back feathers, the impressive zygodactyl toes, and the use of the strong tail feathers to create a firm anchor to the tree. (Zygodactyl toe arrangement refers to the arrangement of the 4 toes of a bird in which the innermost toe has been rotated to point backwards, the 2 middle toes stay pointing forward, and the outermost toe backward, i.e. 2 toes forward and 2 backward, great for gripping tree bark. Seen in woodpeckers and other birds such as parrots.)
In photo #2 I think it is reaching for an acorn stashed earlier in a crevice. A shaky video was then attempted, which shows him extracting the acorn, placing it in the hollowed anvil portion of the snag, and then hammering at it to extract the mast:
The last, #4, shows how the the feet of the woodpecker fully released from the tree as it forcefully drove the bill downward, sort of "action and reaction" I guess.
I presume the Lewis's will remain in the Lake Solano Park area for another month or two, as those birds that elect to migrate will usually leave in late March/April, although most will not travel great distances. This year witnessed many more Lewis's Woodpecker sightings in Californnia's Bay Area than usual.