so how can you state this:

… but when I look at my menu settings after loading the theme the subtext fields are empty

click to enlarge the image:

on top right of your menu options page there is a little flyout ( ps it is on many pages on wordpress sites)
press that button – the flyout does what it says. Mark the description field !
now your menu-items got this extra field.

Wouldn’t it be better to have the navigation below logos?
You have a very extensive navigation.
See here: https://webers-testseite.de/cynthia/mille-deco/

______________

PS : first find an error – maybe on functions.php
how did you implement your ls-slider?
it is just after the slider – so guess it must be an error there. Look on scrolling you can see the content scrolling under the header but a little bit visible on top.
i just select it on your homepage to see it better :

First of all – why dont you use the prestyled child-theme from Enfold? https://kriesi.at/documentation/enfold/child-theme/

you don’t need to include the parent style via functions.php if the style.css of the child-theme is well set up.
This is the content of the style.css of the child-theme:

/*
Theme Name: Enfold Child
Description: A <a href='http://codex.wordpress.org/Child_Themes'>Child Theme</a> for the Enfold WordPress Theme. If you plan to do a lot of file modifications we recommend to use this Theme instead of the original Theme. Updating wil be much easier then.
Version: 1.0
Author: Kriesi
Author URI: http://kriesi.at
Template: enfold
*/

/*Add your own styles here:*/

The template ( is the name of the parent folder ) that is important

The download includes a functions.php file ( empty at the beginning )
on that you can see that there is no closing tag ( ?> )

your line-height on that is very small – in general one takes so approx. 1.5-fold the font-size- try:

.avia-testimonial-name {
    line-height: 36px;
}

if you don’t like that space 30px will be enough too.

PS: if you select the text on the left side you see why the “y” are cut-off:

Clear the cache of Safari. ⌥ ⌘ E
Guess it is only a Problem of that.

you like to have a shrinking logo aswell on mobile devices?

enfold ▸ ⁨js⁩ ▸ ⁨avia-snippet-sticky-header.js

find:
if(shrinking && !isMobile)
replace with:
if(shrinking)

now the shrinking should be there on mobile devices.

To not loose this changing you can have a child-theme : avia-snippet-sticky-header.js
make a copy of that edited js file and – upload it to your child-theme/js folder – because there is on default no js folder – create one.
put this to your child-theme functions.php

add_action( 'wp_enqueue_scripts', 'wp_change_sticky_header_script', 100 );
function wp_change_sticky_header_script() {
   wp_deregister_script( 'avia-sticky-header' );
   wp_enqueue_script( 'avia-sticky-header-child', get_stylesheet_directory_uri().'/js/avia-snippet-sticky-header.js', array('avia-default'), $vn, true);
}

Can i see your site too?
think of – that i’m participant as you – so i can not see private content area.

open the first column in your color-section

that column on church template is a 1/1 container – you see :
click to enlarge the image:

mark that field: “Custom Top and Bottom Margin”
then there will be new input fields – you can have negative Margins on top – thats it

or without that functions.php stuff –
custom link in menu – and give to it the class noMobile menu-item-avia-special
noMobile ( not to be seen in Mobile Menu List)
menu-item-avia-special ( visible on hamburger but on top besides hamburger icon )

the burger nav is not identical to the main-nav. Look to your DOM with some Developer Tools of your browser:
click to enlarge:

this is what happens if you have the hamburger opended.
that hamburger icon and the search icons are part of the main-nav. (b) an are still visible.
the rest fo main-nav is set to display none and the hamburger-menu is now visible.
You see that the list-items are different and have different selectors.
so you can select specific your telefonnumber not to show here: f.e.

#av-burger-menu-ul li.menu-item-30288 {
display: none
}

if you look closely, you will see that with the new enfold (don’t know how long it is now) the main menu items have IDs and the analog hamburger menu items then have the appropriate class.

why don’t you add the phone-number as custom-link to your menu-items.
Dashboard – Appearance – Menus.
Just add a custom-link to your menu and insert .
As Link you put in your: tel:+490654311234567
As Navigation Label what you like f.e. Telephone 06543 – 11234567

but if you like you can do it manually too over an array ( if the amount of pages isn’t so big)
you can use all conditonal tags you know – the tree solution is above – for categories there ar is_category, in_category or has_category etc. pp)

add_filter('avf_logo','av_change_logo');
function av_change_logo($logo){
    if( is_page(21) ) {
    	$logo = "http://www.domain.com/wp-content/uploads/logoforpage21.jpg"; 
    }
  
    elseif ( is_page( array( 42, 54, 6 ) ) ) {
    	$logo = "http://www.domain.com/wp-content/uploads/logoforpage22.jpg"; 
    }

    elseif ( is_page() && !is_page(1307) )  {
    	$logo = "http://www.domain.com/wp-content/uploads/logoforpage23.jpg";  
    }
    return $logo;
}