[clangd] Replace ASTUnit with manual AST management.

Summary:
This refactoring does not aim to introduce any significant changes to
the behaviour of clangd to keep the change as simple as possible.

Reviewers: klimek, krasimir, bkramer

Reviewed By: krasimir

Subscribers: malaperle, cfe-commits

Tags: #clang-tools-extra

Differential Revision: https://reviews.llvm.org/D35406

llvm-svn: 308738