First time install issue: Error HY000/2002

Hello all! First time poster.

I am attempting to install the latest version of WordPress for a client and I’m running into an issue with connecting to the database. I’ve been trying to figure out what is wrong and I am out of ideas:
The environment (latest versions as of 7/24):
CentOS 7, PHP 8, nginx 1.24, MySQL 5.7
This environment is in Google Cloud and both the web server VM and Cloud SQL do not have public IPs. External access to the website is via an external load balancer and the plumbing to connect everything internally have been completed.

I downloaded/extracted the wordpress files into the web root directory and edited the wp-config.php with the relevant data to match my environment. A DB and DB user (w/root DB permissions) were created from the data used in the config file. Navigating to the installer at https://fake-domain.com/wp-admin/install.php and I get the following error:
Error establishing a database connection

I turned on the debug flag and it is reporting “Permission denied”.

If I were to ssh into the VM and execute php commands to connect to the DB, I have no issues. If I hard coded values for mysqli_real_connct() in /wp-includes/class-wpdb.php (line 2019) I get the same error. I’m not sure if WP has some trickery to keep compatibility across various installation scenarios, but I cannot figure it out how to get the site up unless I pull all the code apart.

Below is some evidence of environment make up and findings. Any help/assistance would be greatly appreciated.

Thanks

CentOS:
bash-4.2$ cat /etc/os-release | grep 'PRETTY_NAME'
PRETTY_NAME="CentOS Linux 7 (Core)"

PHP:
bash-4.2$ php -v
PHP 8.2.8 (cli) (built: Jul  4 2023 14:52:54) (NTS gcc x86_64)
Copyright (c) The PHP Group
Zend Engine v4.2.8, Copyright (c) Zend Technologies
    with Zend OPcache v8.2.8, Copyright (c), by Zend Technologies

PHP MYSQL extensions:
bash-4.2$ php -m | grep mysql
mysqli
mysqlnd
pdo_mysql

PHP MySQL client:
bash-4.2$ php -r 'print_r(mysqli_get_client_info()); echo "\n";'
mysqlnd 8.2.8

nginx version:
bash-4.2$ nginx -v
nginx version: nginx/1.24.0

PHP/nginx running as nginx:
bash-4.2$ ps aux | grep nginx | head -5
root      9585  0.0  0.0  49072  1188 ?        Ss   00:59   0:00 nginx: master process /usr/sbin/nginx -c /etc/nginx/nginx.conf
nginx     9586  0.0  0.2  96668  4348 ?        S    00:59   0:00 nginx: worker process
nginx     9587  0.0  0.2  96572  4140 ?        S    00:59   0:00 nginx: worker process
nginx     9599  0.0  1.7 906088 32340 ?        S    00:59   0:00 php-fpm: pool www
nginx     9600  0.0  0.7 510416 14436 ?        S    00:59   0:00 php-fpm: pool www

bash-4.2$ ps aux | grep php-fpm | head -5
root      9598  0.0  1.2 503816 23172 ?        Ss   00:59   0:01 php-fpm: master process (/etc/php-fpm.conf)
nginx     9599  0.0  1.7 906088 32340 ?        S    00:59   0:00 php-fpm: pool www
nginx     9600  0.0  0.7 510416 14436 ?        S    00:59   0:00 php-fpm: pool www
nginx     9601  0.0  0.7 510412 14424 ?        S    00:59   0:00 php-fpm: pool www
nginx     9602  0.0  1.5 906088 29624 ?        S    00:59   0:00 php-fpm: pool www

Logged in user:
bash-4.2$ whoami
nginx

Example web root and file permissions:
bash-4.2$ pwd
/var/www/wpdocs
bash-4.2$ stat wp-config.php | grep 'Access' | head -1
Access: (0644/-rw-r--r--)  Uid: (  997/   nginx)   Gid: (  995/   nginx)
bash-4.2$ stat ../wpdocs/ | grep 'Access' | head -1
Access: (0755/drwxr-xr-x)  Uid: (  997/   nginx)   Gid: (  995/   nginx)

Connectivity to CloudSQL:
bash-4.2$ nping --tcp-connect --dest-port 3306 w.x.y.z

Starting Nping 0.6.40 ( https://nmap.org/nping ) at 2023-07-27 03:04 UTC
SENT (0.0015s) Starting TCP Handshake > w.x.y.z:3306
RECV (0.0026s) Handshake with w.x.y.z:3306 completed
SENT (1.0040s) Starting TCP Handshake > w.x.y.z:3306
RECV (1.0048s) Handshake with w.x.y.z:3306 completed
SENT (2.0062s) Starting TCP Handshake > w.x.y.z:3306
RECV (2.0070s) Handshake with w.x.y.z:3306 completed
SENT (3.0082s) Starting TCP Handshake > w.x.y.z:3306
RECV (3.0091s) Handshake with w.x.y.z:3306 completed
SENT (4.0103s) Starting TCP Handshake > w.x.y.z:3306
RECV (4.0111s) Handshake with w.x.y.z:3306 completed
 
Max rtt: 1.087ms | Min rtt: 0.743ms | Avg rtt: 0.879ms
TCP connection attempts: 5 | Successful connections: 5 | Failed: 0 (0.00%)
Nping done: 1 IP address pinged in 4.01 seconds

PHP script showing CloudSQL version and SQL grants:
bash-4.2$ php -r '$dbcon=mysqli_init();  mysqli_real_connect($dbcon, "w.x.y.z", "temp-user", "fake-password", NULL, NULL, NULL, 0);  $result = $dbcon->query("SELECT VERSION()");  print_r($result->fetch_all());' 
Array
(
    [0] => Array
        (
            [0] => 5.7.42-google-log
        )
)

bash-4.2$ php -r '$dbcon=mysqli_init();  mysqli_real_connect($dbcon, "w.x.y.z", "temp-user", "fake-password", NULL, NULL, NULL, 0);  $result = $dbcon->query("SHOW GRANTS FOR CURRENT_USER");  print_r($result->fetch_all());'
Array
(
    [0] => Array
        (
            [0] => GRANT SELECT, INSERT, UPDATE, DELETE, CREATE, DROP, RELOAD, SHUTDOWN, PROCESS, REFERENCES, INDEX, ALTER, SHOW DATABASES, CREATE TEMPORARY TABLES, LOCK TABLES, EXECUTE, REPLICATION SLAVE, REPLICATION CLIENT, CREATE VIEW, SHOW VIEW, CREATE ROUTINE, ALTER ROUTINE, CREATE USER, EVENT, TRIGGER, CREATE TABLESPACE ON *.* TO 'temp-user'@'%' WITH GRANT OPTION
        )
)

Error logged when attempting to setup WP:
bash-4.2$ tail /var/log/php-fpm/www-error.log 
[26-Jul-2023 21:51:49 UTC] PHP Warning:  mysqli_real_connect(): (HY000/2002): Permission denied in /var/www/wpdocs/wp-includes/class-wpdb.php on line 2019
[26-Jul-2023 22:22:06 UTC] PHP Warning:  mysqli_real_connect(): (HY000/2002): Permission denied in /var/www/wpdocs/wp-includes/class-wpdb.php on line 2019