Oh good question. This is how I would do it:
Step 1:
Create a new custom navigation menu section, called say “Anon Menu” (you can call it whatever you want, but remember the name) and make it a public section (check box at bottom of the modal).
Step 2:
Then in the Common-CSS of a theme or theme component that you create, insert this CSS code. Replace “anon-menu” with the section name-slug of the menu section name you created in step 1 (ie: Custom Section = custom-section).
.sidebar-section-wrapper.sidebar-section[data-section-name="anon-menu"] {
display: none;
}
.anon .sidebar-section-wrapper.sidebar-section[data-section-name="anon-menu"] {
display: block;
}