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

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Harald-R wrote:

@HighCommander4 @kadircet many thanks for the reviews! Added a commit which takes the `QuotedHeaders` filter into account: https://github.com/llvm/llvm-project/pull/140594/commits/7564e9cd65421b5c7e3c6428f7f073fa6f5e3ec5.

There is some duplication with the [logic in the include inserter](https://github.com/llvm/llvm-project/blob/3033f202f6707937cd28c2473479db134993f96f/clang-tools-extra/clangd/Headers.cpp#L307); not sure if this should be solved now or via a dedicated refactoring of the inclusion logic in all places, as was proposed [here](https://github.com/llvm/llvm-project/pull/67749#issuecomment-1904680030). 

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