[clang-tools-extra] [clang-doc] place HTML/JSON output inside their own directories (PR #150655)

[Paul Kirth via cfe-commits]

https://github.com/ilovepi approved this pull request.

Is the plan just to handle this for JSON and Mustache for now, and when we have templates for Markdown (and whatever else) they'll just use this pattern? And I guess migrate any tests we want to keep for HTML once we switch to the mustache implementation by default?

https://github.com/llvm/llvm-project/pull/150655