There was a continuous integration (CI) tool – CruiseControl (2001-2010). Written by ThoughtWorks, the BSD-licensed open-source project got a lot of publicity. http://cruisecontrol.sourceforge.net
They came up with the CCTray format, which has become the de facto standard for describing the status of projects in CI systems: https://cctray.org/v1/
Travis, Jenkins, TeamCity, Drone CI, and many others provide special URLs where they give information about the status of builds, for example:
In Drone CI, that understandably only works for public projects.
Another side of the matter is to make this information available to the user in a convenient form. On macOS, a program called CCMenu does this (see screenshot).