SharePoint ShareGate Migration 2013 > SPO > Home Site Navigation Not Copied

I've recently copied over some List structure and contents with ShareGate and the list navigation experience is the same. 

I haven't been able to recreate the experience on the SPO default home page and have a mix of behaviors occurring between site settings.

The 'site navigation settings' are using the 'classic' style of SP on premise navigation but the modern home page does not display anything listed under 'Current Navigation'. 

Any advice on display 'Current Navigation' from the Old navigation experience on Modern pages is welcome!