Yesterday I ran
Set-SPOHomeSite -HomeSiteUrl /path/to/site to set our home site.
Get-SPOHomeSite indicates that the site mentioned is indeed a home site. I also see that the search bar on top of the home site says "Search in SharePoint", which shows that at least one part of migrating our site to become a home site has worked, but don't see any "My Sharepoint" type of link from the home site to our start page, and our start page never got the same menu header and theme as our home page.
Does anyone know what may be causing this issue?