Building a "hello world" kernel module errors out with "/lib/modules/6.1.2-tinycore/build: No such file or directory"

Question

I'm running Tinycore 6.1.2 and writing a simple kernel module that prints out hello world to the message buffer of the kernel. This is the code I'm using.

// test_module.c 

/*
 * test module.
 */

#include <linux/module.h>
#include <linux/init.h>

MODULE_LICENSE("GPL");

static int __init initialization_routine(void) {
    printk("Hello, world!\n");
    return 0;
}

static void __exit cleanup_routine(void) {
    printk("Unloading module!\n");
}

module_init(initialization_routine);
module_exit(cleanup_routine);

My Makefile is as follows

obj-m += test_module.o

KDIR := /lib/modules/$(shell uname -r)/build

all:
        make -C $(KDIR) M=$(PWD) modules

clean:
        make -C $(KDIR) M=$(PWD) clean

What am I doing wrong? Thanks.