Change in keyframe interpolation didn't reflect on the graph editor

Beginner here, I was trying to understand keyframe interpolation and how it affects the graph in the graph editor.

I made a simple motion animation, where an airplane moved from one point to another in a straight line. Created two keyframes at t=0 and t=3s, and by default the interpolation between them was linear. On the graph editor the value graph looked like this: x values went from 200 to 1500 in 3s, y values stayed the same (as there was no motion in y).

I selected the two keyframes on the timeline (which were looking like diamonds) and then right clicked -> keyframe interpolation, and changed the temporal interpolation to Bezier. This changed the keyframes to hourglass icons on the timeline. However, when I opened the graph editor the value graph was exactly the same as was for the linear interpolation. I was expecting it would change to the curve that you get when you "ease in" and "ease out".

Sure I'm able to make the graph look like how I want to by going to the graph editor and then clicking on the "easy ease" icon in the editor itself. But I was just hoping if I've understood keyframe interpolation correctly changing the interpolation of the keyframes from linear to Bezier should automatically reflect on the graph editor.

(Screen recording attached, for some reason the recording software didn't record the context menus, where clicked on keyframe interpolation and selected Bezier in the temporal interpolation)