It sounds like there may be some configuration or permission issues with your Home site and Viva Connections deployment. Here are a few things you can try to troubleshoot the issue:
Check the site permissions: Make sure that the user has the necessary permissions to access the home site and the other SharePoint sites in the global navigation. Check the site permissions for the Home site, the Viva Connections site, and the other SharePoint sites in the global navigation.
Check the global navigation settings: Make sure that the global navigation is configured correctly and that the links are pointing to the correct sites. Check the global navigation settings for the Home site and the other SharePoint sites in the global navigation.
Check the Viva Connections configuration: Make sure that the Viva Connections web part is configured correctly and that the links are pointing to the correct sites. Check the Viva Connections configuration settings.
Check the Teams settings: Make sure that the Teams settings are configured correctly and that the Home site is set up as the default landing page. Check the Teams settings for the Home site.
Check the web part permissions: Make sure that the user has the necessary permissions to view the web parts on the Home site and the other SharePoint sites in the global navigation. Check the web part permissions for the Home site and the other SharePoint sites in the global navigation.