Is there a Team Foundation Server GUI client that has visual branches?

Bourgeon. Available for Visual Studio 2013, 2015, 2017, 2019.

https://marketplace.visualstudio.com/items?itemName=StefanLober.Bourgeon

Obviously the author is a git user who was forced to use TFS.

You can View the Branch Hierarchy of a Team Project by go to Source Control Explorer, click the branch from which you want to begin to explore your branch structure after that, Click the File menu, point to Source Control, point to Branching and Merging, and then click View Hierarchy.

View the Branch Hierarchy of a Team Project

You can use the branching and "track changes" visualizations. See the blog post below for details:

http://www.edsquared.com/2010/03/17/Branching+And+Track+Changes+Visualization+In+TFS+2010+Is+Awesome.aspx