[clangd] Actually parse Index section of the YAML file.
This fixes a bug in dbf486c0de92c76df77c1a1f815cf16533ecbb3a, which
introduced the Index section of the config, but did not register the
parse method, so it didn't work in a YAML file (but did in a test).
Differential Revision: https://reviews.llvm.org/D87710
(cherry picked from commit 7029e5d4ca20d20982da8efe89de27acd8d7d75b)