Is there a way to get the installed version of TFS 2017 when I only have access to its web interface via HTTP?
There's an "About" link that appears on every page in the top right corner. It may be hidden within an ellipsis menu (...).
You'll get a version number there, like 15.112.26307.0.
The list for 2015 onward is:
Team Foundation Server 2015.
Team Foundation Server 2017.
Team Foundation Server 2018.
Ref: https://docs.microsoft.com/en-us/azure/devops/release-notes/features-timeline#server-build-numbers