MB3 182a: Leaning on or Using a Tree on Shabbos (336:12-13)

A tree with dried up fruit is still subject to תולש on Shabbos. Uprooting dried grass on Shabbos. Onions, etc. which take root not in the ground.

Using the "sides of a tree" (something attached to/leaning on a tree) on Shabbos vs. using something attached to something else that's attached to the tree (צדי צדדים).

Leaning on a strong tree on Shabbos is permissible as long as it won't move.