My default view is Sidebar off. When I tap the button, an ad is displayed top center that covers the existing ad. I have a feeling this isn't supposed to work this way.
Weird! I'm on iPadOS 13.5.1 using Safari, no extensions. I quit and retested and Sidebar (+ad) still disappears upon page reload.
Added: on the iPad it's the desktop version as you probably know. Switching to the mobile version produces the same behavior. Also Sidebar disappears when clicking anywhere on the page while it's open except on the Sidebar itself.