function addKeyDownHandlerForTelerikFilterMenu() {
    document.body.addEventListener("keydown", function (event) {
        if (event.key === "Enter") {
            if (event.target.classList.contains("k-input-inner") && event.target.closest(".k-filter-menu-container")) {
                const filterMenuContainer = event.target.closest(".k-filter-menu-container");
                const filterButton = filterMenuContainer.querySelector(".k-button-solid-primary");
                if (filterButton) {
                    filterButton.click();
                }
            }
        }
        if (event.key === "Delete") {
            if (event.target.closest(".k-filter-menu-container")) {
                const filterMenuContainer = event.target.closest(".k-filter-menu-container");
                const clearButton = filterMenuContainer.querySelector('button[type="reset"]');
                if (clearButton) {
                    clearButton.click();
                }
            }
        }
    });
}

And in my MainLayout.razor I added this:
protected override async Task OnAfterRenderAsync(bool firstRender)
{
    if (firstRender)
    {
        await JsRuntime.InvokeVoidAsync("addKeyDownHandlerForTelerikFilterMenu");
    }

    await base.OnAfterRenderAsync(firstRender);
}

Now I can confirm any input in a textfield of the filtermenu with ENTER and this will perform a click on the Filter-Button.
If the focus is set to a FilterMenu and I hit the DEL-Key, a click on the Clear-Button is performed.