This appears to be a bug. Without any branding applied and using SharePoint 2016 On-Prem, when I enable the Portal site Connection on a Team site, the App Launch bar disappears and I don't see any breadcrumb to get to the Portal site.
Bismarck
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Sign up to join this communityI'm unable to reproduce this issue. I've added a Portal Site connection on a Team site to another Site Collection within the same Web Application (just a Publishing site in my case) and the Suite Nav is still present.