The other day I had put the Git install folder in the PATH. That didn't work. Today I put the Git bin folder in my PATH. This way, there's still no Browse button, but the fields get populated automatically with the system settings and the other buttons are enabled. So that will work for me.

I wouldn't be surprised if someone misguidedly decided there was no need for a Browse button as everyone who uses Git should have it in their PATH. I'm tempted to pull the source code to look at it...

So I did. The logic for the Browse button was removed from module ConfigurationEditorComponent.java in this EGit commit with comment,
"Follow up on commit d7a447 in jgit which removed gitprefix logic and broke egit compile."

The corresponding jgit commit states: "The only purpose of the gitprefix logic was to determine the path to the system-wide config file. This is now done by discoverGitSystemConfig() independent of the gitprefix, so get rid of this unused code."

And another related jgit update states:
"Now that d7a4473 removed the gitprefix property, we did not have a way to specify the path to the Git system config file in case discoverGitSystemConfig() fails. Fix that by introducing a member variable that caches the result of discoverGitSystemConfig() as well as a setter method to overwrite the content of that variable."

Can't say that I understand all of that. But I'm satisfied that the button wasn't simply removed on a whim.