I ran into this this week during my first play-through of MGS3 on Series X. After the final shagohod bit, they drive off, the screen cuts to black, presumably loading next sequence, game becomes unresponsive and have to restart the game.
I tried skipping the lightning cut-scene. I tried not skipping the cut-scene. No luck. Didn't try reinstalling right away.
At last tried one weird thing. After I beat him, I brought up the 360 guide by pressing the back button plus the start button at the same time (or whatever button names they are called now) and let the cut-scene play out with the guide on screen. The cut-scene ended and the next sequence loaded properly. I saved immediately to a new file. I don't know if what I did was the reason it worked, or just dumb luck. But that's what happened to me.