Link to test case: I can not give, because my project runs under XAMPP on my local machine
Debugger code (debug.datatables.net):

my data.admin.user.js

$(document).ready(function() {

    var userdataTable = $('#userList').DataTable(
        {
            lengthMenu: [
                [25, 50, 100],
                [25, 50, 100],
            ],
            lengthChange: false,
            pageLength: 50,
            processing: true,
            serverSide: true,
            searching: true,
            search: {
                return: true,
            },
            paging: true,
            info: false,
            dom: 'lrtip',          
            language: {
                lengthMenu: 'Zeige _MENU_ Einträge pro Seite',
                zeroRecords: 'Nichts gefunden - Tut mir leid',
                info: 'Zeige Seite _PAGE_ von _PAGES_',
                infoEmpty: 'Keine Daten verfügbar',
                infoFiltered: '(gefiltert von _MAX_ Einträgen)',
                search: 'Suche: ',
                previous: 'vorher',
                next: 'nächster',
            },
            ajax: {
                url: "action.php",
                type: "POST",
                data: { action: 'userList'},
                dataType: "json"
            }
        }
    );

    $('#userSearch').on('keyup', function() {
        userdataTable.search($(this).val()).draw();
    });
} );

action.php

if(!empty($_POST['action']) && $_POST['action'] == 'userList'){
    $phoenix->getUserList();
}

phoenix.php

    public function getUserList(){
        $sqlUnfiltered = "SELECT usr.*, grp.Name AS Gruppenname, grp.Is_Admin FROM tbl_user AS usr
                LEFT JOIN tbl_usergroups AS usrgrp ON usr.ID = usrgrp.UserID
                LEFT JOIN tbl_groups AS grp ON usrgrp.GroupID = grp.ID ";

        $sql = $sqlUnfiltered;  

        // Suchkriterium
        if(!empty($_POST['search']['value'])){
            $sql .= "WHERE";
            $sql .= " (usr.id LIKE '%" . $_POST['search']['value'] . "%')";
            $sql .= " OR (usr.name LIKE '%" . $_POST['search']['value'] . "%')";
            $sql .= " OR (grp.name LIKE '%" . $_POST['search']['value'] . "%')";
        }

        // Sortierung
        if(!empty($_POST["order"])){
            $sql .= " ORDER BY " . $_POST["order"][0]["column"] + 1 . " " . $_POST["order"][0]["dir"] . " ";
        } else {
            $sql .= " ORDER BY id ASC";
        }

        // Limitierungen
        if (!empty($_POST["length"])){
            $sql .= " LIMIT " . $_POST["start"] . ", " . $_POST["length"];
        }

        $result = mysqli_query($this->dbConnect, $sql);
        $resultUnfiltered = mysqli_query($this->dbConnect, $sqlUnfiltered);
        $rowsCountFiltered = mysqli_num_rows($result);
        $rowsCountUnfiltered = mysqli_num_rows($resultUnfiltered);
        $userData = array();
        
        while( $user = mysqli_fetch_assoc($result)){

            if($user['Aktiv'] == 'Y'){
                $AktivHTML = '<label class = "form-check form-switch"><input class="form-check-input" type="checkbox" checked disabled></input></label>';
            } else {
                $AktivHTML = '<label class = "form-check form-switch"><input class="form-check-input" type="checkbox" disabled></input></label>';
            }

            if($user['Is_Admin'] == 'Y'){
                $IsAdminHTML = '<label class = "form-check form-switch"><input class="form-check-input" type="checkbox" checked disabled></input></label>';
            } else {
                $IsAdminHTML = '<label class = "form-check form-switch"><input class="form-check-input" type="checkbox" disabled></input></label>';
            }
            
            $aktionen = '<div class="btn-list flex-nowrap">';
            $aktionen .= '<a href="#" class="btn">Bearbeiten</a>';
            $aktionen .= '<a href="#" class="btn">L&ouml;schen</a>';
            $aktionen .= '</div>';

            $userRows = array();
            $userRows[] = $user['ID'];
            $userRows[] = $user['Name'];
            $userRows[] = $user['EMail'];
            $userRows[] = $AktivHTML;
            $userRows[] = $user['Gruppenname'];
            $userRows[] = $IsAdminHTML;
            $userRows[] = $aktionen;
            $userData[] = $userRows;
        }

        $output = array(
            "draw"              =>  1,
            "recordsTotal"      =>  $rowsCountUnfiltered,
            "recordsFiltered"   =>  $rowsCountFiltered,         
            "data"              =>  $userData
        );

        echo json_encode($output);
        
    }

Error messages shown:

No error messages

Description of problem:

My problem is that the datatable do not filter the result after I enter a search key. With the developertools in Chrome I see that my search key works. In the response you get only 1 item back from 3 items in total, but in my datatable you will see all items.

I try to get a solution for 3 days and I have no idea where I have the failure.

Please can you help me?

Edited by Colin - Syntax highlighting. Details on how to highlight code using markdown can be found in this guide.