Using kfunc defined in a loadable module by BPF program

I would like to define my own custom kfunc (in a loadable linux kernel module) that I can then use in a bpf program. I think I'm 99% there, but I'm stuck on loading the bpf program with bpftool. What I see is:

libbpf: failed to find BTF for extern 'foo_bar': -3

The foo_bar is my custom kfunc (see below). I do not understand where the symbol is looked for...

Reproduction

$ make
make -C /lib/modules/6.16.2-zen1-1-zen/build M=/home/xyz modules
make[1]: Entering directory '/usr/lib/modules/6.16.2-zen1-1-zen/build'
make[2]: Entering directory '/home/xyz'
  CC [M]  kfoo.o
  MODPOST Module.symvers
  CC [M]  kfoo.mod.o
  CC [M]  .module-common.o
  LD [M]  kfoo.ko
  BTF [M] kfoo.ko
make[2]: Leaving directory '/home/xyz'
make[1]: Leaving directory '/usr/lib/modules/6.16.2-zen1-1-zen/build'

$ sudo insmod kfoo.ko

$ strings /sys/kernel/btf/kfoo
foo_bar
bpf_kfunc
kfoo_exit
kfoo_init
regs

$ clang -Wall -Werror -O2 -target bpf -c foo_bpf.c -o foo_bpf.o

$ sudo bpftool prog load foo_bpf.o /sys/fs/bpf/foo_bpf autoattach
libbpf: failed to find BTF for extern 'foo_bar': -3
Error: failed to open object file

The sources I'm using are below.

foo_bpf.c

#include <linux/bpf.h>
#include <bpf/bpf_helpers.h>
#include <bpf/bpf_tracing.h>
#include <asm/ptrace.h>

extern int foo_bar(struct pt_regs *regs);

SEC("uretprobe//tmp/app:foo")
int foo_bar_call(struct pt_regs *ctx) {
    foo_bar(ctx);
    return 0;
}

char _license[] SEC("license") = "GPL";

kfoo.c

#include <linux/module.h>
#include <linux/kernel.h>
#include <linux/btf.h>

__bpf_kfunc int foo_bar(struct pt_regs *regs);

__bpf_kfunc_start_defs();

__bpf_kfunc int foo_bar(struct pt_regs *regs)
{
    pr_err("foo_bar\n");
    return 0;
}

__bpf_kfunc_end_defs();

BTF_KFUNCS_START(kfunc_foo_bar)
BTF_ID_FLAGS(func, foo_bar)
BTF_KFUNCS_END(kfunc_foo_bar)

static const struct btf_kfunc_id_set foo_bar_set = {
    .owner = THIS_MODULE,
    .set   = &kfunc_foo_bar,
};

static int __init kfoo_init(void)
{
    int ret;
    ret = register_btf_kfunc_id_set(BPF_PROG_TYPE_KPROBE, &foo_bar_set);

    pr_err("%s: %d\n", __func__, ret);
    return ret;
}

static void __exit kfoo_exit(void)
{
    pr_err("%s: bye\n", __func__);
}

MODULE_LICENSE("GPL");

module_init(kfoo_init);
module_exit(kfoo_exit);

Makefile

obj-m += kfoo.o

all:
    make -C /lib/modules/$(shell uname -r)/build M=$(PWD) modules

clean:
    make -C /lib/modules/$(shell uname -r)/build M=$(PWD) clean