[clang-tools-extra] Make clang print include paths without `../` jumps

See https://github.com/llvm/llvm-project/pull/167020#discussion_r2505506435.
We essentially need to remove this line:
https://github.com/llvm/llvm-project/blob/5e4505d562528992e25792463affb23518cacf86/clang-tools-extra/clang-tidy/.clang-tidy#L3

Start with clang-tools-extra/clang-tidy/.clang-tidy at line 3 and read the linked pull-request discussion for the intended behavior. Remove the referenced configuration line, then verify that clang prints include paths without ../ jumps.

Written by the indexing model from the issue text.