Не могу решить проблему с синтаксисом sql?
Можно так:
<?php

require_once 'vendor/connect.php';

$login = mysqli_real_escape_string($connect, $_SESSION["login"]);

$query = mysqli_query($connect, "SELECT * FROM `users` WHERE login = '$login'");

$balance = mysqli_fetch_assoc($query);

echo 'Balance:' . $balance['balance']. PHP_EOL;

if(isset($_POST['click'])) {
	mysqli_query($connect, "UPDATE `users` SET `balance`=`balance`+0.001 WHERE login = '$login'");
	echo 'New balance:' . ($balance['balance'] + 0.001) . PHP_EOL;
}

?>

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А лучше так:

<?php

require_once 'vendor/connect.php';

/* prepare statement */
$stmt = $connect->prepare("SELECT `balance` FROM `users` WHERE login = ? ");

/* bind parameters for login */
$stmt->bind_param("s", $_SESSION["login"]);

/* execute query */
$stmt->execute();

$stmt->bind_result($balance);

/* fetch value */
$stmt->fetch();

/* free result to next use */
$stmt->free_result();

echo 'Balance:' . $balance . PHP_EOL;

if (isset($_POST['click'])) {

	/* prepare statement */
	$stmt = $connect->prepare("UPDATE `users` SET `balance`=`balance`+0.001 WHERE login = ? ");

	/* bind parameters for login */
	$stmt->bind_param("s", $_SESSION["login"]);

	/* execute query */
	$stmt->execute();

	echo 'New balance:' . ($balance['balance'] + 0.001) . PHP_EOL;
}

?>

Test PHP code online
Можно так:
<?php

require_once 'vendor/connect.php';

$login = mysqli_real_escape_string($connect, $_SESSION["login"]);

$query = mysqli_query($connect, "SELECT * FROM `users` WHERE login = '$login'");

$balance = mysqli_fetch_assoc($query);

echo 'Balance:' . $balance['balance']. PHP_EOL;

if(isset($_POST['click'])) {
	mysqli_query($connect, "UPDATE `users` SET `balance`=`balance`+0.001 WHERE login = '$login'");
	echo 'New balance:' . ($balance['balance'] + 0.001) . PHP_EOL;
}

?>

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А лучше так:

<?php

require_once 'vendor/connect.php';

/* prepare statement */
$stmt = $connect->prepare("SELECT `balance` FROM `users` WHERE login = ? ");

/* bind parameters for login */
$stmt->bind_param("s", $_SESSION["login"]);

/* execute query */
$stmt->execute();

$stmt->bind_result($balance);

/* fetch value */
$stmt->fetch();

/* free result to next use */
$stmt->free_result();

echo 'Balance:' . $balance . PHP_EOL;

if (isset($_POST['click'])) {

	/* prepare statement */
	$stmt = $connect->prepare("UPDATE `users` SET `balance`=`balance`+0.001 WHERE login = ? ");

	/* bind parameters for login */
	$stmt->bind_param("s", $_SESSION["login"]);

	/* execute query */
	$stmt->execute();

	echo 'New balance:' . ($balance['balance'] + 0.001) . PHP_EOL;
}

?>

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