Well, the issue is that you can't connect to MySQL with the account/credentials you've used so far.
It's not a question of supporting non-WP-specific software or not, the MySQL account simply isn't working. 🤷♂️
You could upload a simple PHP script that tries to connect to MySQL with the same account to prove your point I guess. Here's an example code:
<?php
$servername = "localhost";
$username = "username";
$password = "password";
$database = "database";
// Create connection
$conn = new mysqli($servername, $username, $password, $database);
// Check connection
if ($conn->connect_error) {
die("Connection failed: " . $conn->connect_error);
}
echo "Connected successfully";
// Close connection
$conn->close();
If they still won't help, it's probably time to change hosting... 🙄