c_cpp_properties.json is a configuration file specific to Microsoft's C/C++ VSCode plugin. It's not used by clangd or clang-tidy.
Clangd and clang-tidy use compile_commands.json for configuration. Please see https://clangd.llvm.org/installation#compile_commandsjson for some discussion of this file and how to generate it.
vscode extensions - Visual Studio Code Clangd only use clang-tidy for project. Problems with external include - Stack Overflow
VS Code - clang-tidy support in C/C++ extension
c++ - How can I tell VS Code Cpptools' clang-tidy support to use the compile_commands.json generated with CMake? - Stack Overflow
clang-tidy support in VSCode is possible
Look at vscode-clangd. The code-completion seems more robust (as long as you have suitable compile-commands.json) and it supports clang-tidy.
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if you're an exceptionally attractive individual like me, the only things preventing you from retiring clion and adopting vscode (for everything) are clang-tidy and cppcheck. we can get clang-tidy by upvoting this feature request for adding clang-tidy support to the cpp extension for vscode: https://github.com/microsoft/vscode-cpptools/issues/2908
clang-tidy good. more clang-tidy.