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

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Harald-R wrote:

> But since we have both config options, maybe there is a reason for overwrites in this direction as well.

Hmm, I was mainly focusing on the quoted -> angled case, hence why only the `AngledHeaders` filter is used. But I have to agree that following the config fully makes sense. I see other instances, like `IncludeInserter::calculateIncludePath` do make use of both filters. I can make the change, to overwrite the inclusion style when the configs dictate that, if that is the desired behavior here.

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