Your public key looks fine. I believe the error you are getting might be related to the private key which you set to NULL. Try passing your private key to libssh2, and make sure to add your public key to the servers authorized keys.

Reproducing the problem

I've tried reproducing the error, but it seems to work for me, below I will describe how I did it, and some speculations regarding your problem:

1. Made a directory and copied in the example file sftp_write.c from libssh2.
2. Changed auth_pw from 1 to 0 on line 27.
3. Changed pubkey and privkey to use my own keys, and added debugging.

    const char *pubkey = "/home/user/.ssh/id_rsa_PEM.pub";
    const char *privkey = "/home/user/.ssh/id_rsa_PEM";
    int liberr;
    if(liberr = libssh2_userauth_publickey_fromfile(session, username,
                                               pubkey, privkey,
                                               password)) {
        fprintf(stderr, "\tAuthentication by public key failed: %d\n", liberr);
        goto shutdown;
    }

4. changed

#include "libssh2_config.h"
#include <libssh2.h>
#include <libssh2_sftp.h>

#ifdef HAVE_WINSOCK2_H
# include <winsock2.h>
#endif
#ifdef HAVE_SYS_SOCKET_H
# include <sys/socket.h>
#endif
#ifdef HAVE_NETINET_IN_H
# include <netinet/in.h>
#endif
# ifdef HAVE_UNISTD_H
#include <unistd.h>
#endif
#ifdef HAVE_ARPA_INET_H
# include <arpa/inet.h>
#endif

to

#include <libssh2.h>
#include <libssh2_sftp.h>

#include <sys/socket.h>
#include <netinet/in.h>
#include <unistd.h>
#include <arpa/inet.h>

To match my setup.

5. Used Docker to compile the image by running

docker run -i --rm \
    -w $(pwd) -v $(pwd):$(pwd) \
    -v /etc/passwd:/etc/passwd:ro  \
    -v /etc/group:/etc/group:ro \
    -u $(id -u):$(id -u) \
    datafr/libssh2:latest \
    gcc -g -I /usr/include/ -L /usr/lib/ -l ssh2 sftp_write.c -o a.out

6. Ran the program with

./a.out 127.0.0.1 $USER

Results

Running this code results in error -19: LIBSSH2_ERROR_PUBLICKEY_UNVERIFIED. This is because the docker image uses an older version of libssh2 which requires older PEM keys. This is fixed by creating a new keypair with

ssh-keygen -m PEM -t rsa -P "" -f id_rsa_PEM

And modifying the code to use the new keys.

Running the code once more gives us error -18: LIBSSH2_ERROR_AUTHENTICATION_FAILED. This is fixed by adding our new public key id_rsa_PEM.pub to the servers authorized_keys-file.

After this, we get no more errors, and the output looks like this:

$ ./a.out 127.0.0.1 $USER
Fingerprint: XXXXXXX
libssh2_sftp_init()!
libssh2_sftp_open()!
libssh2_sftp_open() is done, now send data!
all done

And I can confirm the creation of a file called /tmp/TEST containing our code from sftp_write.c.

Further speculations

I've noticed that error -16: LIBSSH2_ERROR_FILE occurs when the file is either non-existent or has the wrong permissions, so I'll ask you to double check your file permissions. I'll post my own permissions as reference.

Client ~/.ssh/ directory:

$ ls -alh
total 28K
drwx------  2 user user 4,0K Sep 28 15:37 .
drwxr-xr-x 32 user user 4,0K Sep 28 15:36 ..
-rw-rw-r--  1 user user 2,7K Sep 28 15:36 config
-rw-------  1 user user 2,5K Sep 28 15:36 id_rsa_PEM
-rw-r--r--  1 user user  574 Sep 28 15:36 id_rsa_PEM.pub
-rw-------  1 user user 6,3K Sep 28 15:36 known_hosts

Server ~/.ssh/ directory:

$ ls -alh
total 20K
drwx------  2 user user 4,0K Sep 28 15:39 .
drwxr-xr-x 32 user user 4,0K Sep 28 15:39 ..
-rw-------  1 user user 3,4K Sep 28 15:39 authorized_keys