I don't see the Branches link in Azure DevOps in the Repos menu:
The Azure admin has confirmed that I'm in the Contributor group and I can access branches through Visual Studio Team Services.
I haven't been able to find the setting that will let me manage branches in Azure DevOps / visualstudio.com.
ANSWER:
So dumb... I needed to change this dropdown from the TFVC project in the Azure DevOps header:
To the Git repo:
And now I see options for Branches and Pull Requests in my Repos sub-menu: