Correct answer is already there to answer the question. I want to mention new JavaScript API PerformanceNavigationTiming, it's replacing deprecated performance.navigation.
Following code will log in console "back_forward" if user landed on your page using back or forward button. Take a look at compatibility table before using it in your project.
var perfEntries = performance.getEntriesByType("navigation");
for (var i = 0; i < perfEntries.length; i++) {
console.log(perfEntries[i].type);
}