In Pathfinder 2e, do tiny animals get a circumstance bonus to AC? Would a Tiny familiar get that same bonus?
Per the CRB index, all rules about Tiny creatures appear on p473-475. Those pages include information about sharing space and moving through other creatures' space, but do not include anything about ability or AC alterations.
Furthermore, a Search of the PDF reveals a lot of references to parts of items and objects being tiny, references that Familiars and Leshy Familiars are Tiny, and (perhaps the most relevant) Tiny carrying capacity and the Bulk of a Tiny creature on p295.
However, probably the greatest indicator that there is no inherent (numerical) benefit for being a different size are the spells Shrink and Enlarge. Shrink applies no penalty beyond restricting your Reach, and Enlarge applies a damage increase and Clumsy 1 to make it a "buff" spell. There are no references to size bonuses, or the benefits of a creature that size (that aren't explained in the spell).