This reduces the size of the dependency graph and makes incremental
development a little more pleasant (less rebuilding).
This introduces a bit of complexity/fragility as some tests verify
clang-tidy behavior. I attempted to isolate these and build/run as much
of the tests as possible in both configs to prevent rot.
Expectation is that (some) developers will use this locally, but
buildbots etc will keep testing clang-tidy.
Fixes https://github.com/clangd/clangd/issues/233
Differential Revision: https://reviews.llvm.org/D105679