Can I keep the other menu items visible while Display Mode is expanded?

Yes. Open Settings > Menu > Menu Appearance & Behavior > Additional Menu Options… and turn off Hide other unexpanded menu items under Expanding Menu Items.

By default, expanding a submenu such as Display Mode temporarily hides other items in that display’s menu block to keep the menu compact. Turning this option off keeps those other items available alongside the expanded content. The option applies when the menu uses inline expansion.

See Menu Appearance & Behavior for related choices, including whether expanded content stays open the next time you open the App Menu.