[clang-tools-extra] Follow style configuration in clangd when inserting missing includes (PR #140594)

[kadir çetinkaya via cfe-commits]

kadircet wrote:

just a high level question, I wasn't following the recent developments closely, but we seem to have both an `AngledHeaders` and `QuotedHeaders` option. Why are we only following one here?

I guess the signals for angled includes are much stricter (search paths need to be marked with `-isystem`), hence we don't need to overwrite an angle back to a quote. But since we have both config options, maybe there is a reason for overwrites in this direction as well.

https://github.com/llvm/llvm-project/pull/140594