When inline function definition and extern function declaration are all present in one .c file, no link error is observed

Even though this might look like duplication, I'd claim that it isn't.

Why does a compiler make the Foo function, which is defined in foo.c as inline double Foo() { return 1.2; }, a global function if the foo.c file also has the extern double Foo(); line anywhere?

Please see the example with foo.c and main.c:

// foo.c
#if defined(WITH_DECL)
extern double Foo();
#endif

inline double Foo() {
  return 1.2;
}

double Bar() {
  printf("%lf\n", Foo());
  return Foo() + Foo();
}

And,here's main.c:

double Foo();
double Bar();
int main() {
  printf("Bar + Foo = %lf + %lf\n", Bar(), Foo());
  return 0;
}

Here's how I built:

clang -O2 main.c foo.c
clang -O2 main.c foo.c -DWITH_DECL

The first command failed. The second command silently succeeded.

I understand why the first failed. As expected it's a linker error:

clang -g3 -O0 -std=c11 foo.c main.c -Wall -Werror -O2
/usr/bin/x86_64-pc-linux-gnu-ld.bfd: /usr/bin/x86_64-pc-linux-gnu-ld.bfd: DWARF error: mangled line number section (bad file number)
/tmp/main-10e175.o: in function `main':
/home/aion1223/workspace/prac/main.c:7:(.text+0x8): undefined reference to `Foo'
clang: error: linker command failed with exit code 1 (use -v to see invocation)`

I do not understand why the second command does not fail.

First, do I expect this to happen for all standard-complying compilers? Second, why at least some of my compilers silently build the executable when -DWITH_DECL is given?

I'd like to figure out if this is something that I can rely on, or it just happened so but is not guaranteed by C language standard.

The standard I tried is c99, c11, and c17. The compilers are clang 20, gcc14, and gcc12.