[clangd] Correctly identify self-contained headers included rercursively

Right now when exiting the file Headers.cpp will identify the recursive
inclusion (with a new FileID) as non self-contained and will add it to the set
from which it will never be removed. As a result, we get incorrect results in
the IncludeStructure and Include Cleaner. This patch is a fix.

Reviewed By: sammccall

Differential Revision: https://reviews.llvm.org/D124166