Auto Including c++ headers in .c files

[hagz0r]

Check for existing issues

• Completed

Describe the bug / provide steps to reproduce it

When writing C code and trying to use a certain function/variable defined in C headers, Zed will auto include the C++ header, instead of C version.

Zed Version and System Specs

Zed: v0.166.0 (Zed Preview)
OS: Linux Wayland arch unknown
Memory: 14.8 GiB
Architecture: x86_64
GPU: NVIDIA GeForce RTX 4070 Laptop GPU || NVIDIA || 565.77

If applicable, add screenshots or screencasts of the incorrect state / behavior

If applicable, attach your Zed.log file to this issue.

N/A

[SomeoneToIgnore]

See #14411 (comment) for a potential solution.

Duplicate of #14660 (talks about autocompletion, but the reason is the same — clangd by default uses C++ not C).