I was able to record my screen while opening an RStudio project with a Git repository that I have been using for a couple of years. A few seconds after the RStudio window appears, this blank window pops up and then disappears:
A few seconds later, this window appears then disappears:
A few seconds after that, this window appears then disappears:
That is the path to the file folder with the .Rproj file, the Git repo, and all the rest of the project's files.
A few seconds after that, this window appears then disappears:
That's all the action for about 30 seconds, and then the windows with the Git version and the message about the unrecognized program appear and disappear in very rapid succession.
Finally, when I go in Windows Explorer to that folder and invoke "Git Bash Here" via the right-click menu, and run "git status", this is the result:
The prompt is my computer's name, the mysterious "MINGW64" designation, which does correspond to a directory name under the Git directory, and then the folder path, followed by the branch name. The repositories all seem to behave as expected using Git Bash or Git Gui.