[clang-tools-extra] reapply [clang-doc] Add --asset option to clang-doc (PR #96358)

[Paul Kirth via cfe-commits]

ilovepi wrote:

The two complementary patches, making the test free standing, and fixing the default asset path to be `share/clang-doc` have landed now. Can you update your patch, and resolve conflicts. If that passes CI, then I think we're probably about ready to reland.

https://github.com/llvm/llvm-project/pull/96358