Return true to jquery from php file

You are doing it wrong.

The .load() method is asynchronous and does not return the value from the server (it returns the element that it was called on: $("#lvlupann")), so using the returned value in an if statement does not make sense.

You have to wait for the request to finish before you can use the value, like so:

$("#lvlupann").load("/templ/checknlvl.php", function (value) {
    if (value == true) {
        $("#lvlupann").addClass("nlvlann");
    }
});

As for the PHP file, the return true; will just stop the script. It does not send anything to the client. In order to send two or more things from PHP to the client you need to package the output in some fashion.

The $.get method would be useful:

$.get('/templ/checknlvl.php').done(function (data) {
    $("#lvlupann").html(data.content);
    if (data.success) {
        $("#lvlupann").addClass("nlvlann");
    }
});

<?php
echo json_encode([
    'content' => '<strong>Some content...</strong>',
    'success' => true,
]);
die;

If all you want to do is get a boolean value from the PHP script then something like this would do it:

$.get('/templ/checknlvl.php').done(function (value) {
    if (value === "true") {
        $("#lvlupann").addClass("nlvlann");
    }
});

<?php
if (1 == 1) {
    echo 'true';
} else {
    echo 'false';
}
die;