Thanks again for the follow-up!
This still happens in Firefox, incognito browsers, and I’ve cleared the website server cache in addition to my local. Can also confirm the client on a different machine and IP address is experiencing the same; no menu printed from Safari on iPad, but menu prints on all desktop browsers.
To see if the browser was taking in the CSS at all, I added “visibility: hidden;” and it removes the menu content from being displayed, but leaves the same white space it would have taken up in the print. I’m not sure why “display: none;” isn’t working.