The claim about Willie Lincoln that is most fully developed in the passage is:
2. Willie's "self-possession... was extraordinary."
The passage provides a detailed account of a specific incident where Willie interacts with prominent figures (Secretary Seward and Prince Napoleon) in a composed and dignified manner, demonstrating his remarkable self-possession. The author describes how Willie is not overwhelmed by the attention and is able to respond with grace and confidence, which highlights the extraordinary nature of his composure and demeanor.