What concerns where white could have played better, I guess both players played weak and
better moves could be found on almost every move.
For example, on move 28, instead of 28. h4, white could have played 28. Qh5 Qh7 29. Qg4 Qg6 30. Qh4 Qh7 31. Qa4, picking up a pawn for free.
This might have been sufficient for an easier win.
So... a Grandmaster and a Senior Master are playing a game using their engines with a 40 days/10 moves time control, and they are playing weak moves...
I wonder what you've been smoking, sir.
Black has no issues in your line, e.g. 29...Kf8 (instead of 29...Qg6), or 31...Qh6 at the end of the line. He is certainly not worse.
You suggested black could take on c7, that is why my Kd5 line.
Because of Ra8, however, which requires calculation, my preferred move would be
Kc4, as I pointed out, and then one black pawn falls, while the rook is still unactive.
I suggested 54...Rxc7 after 54.f4 (taking at d8 looks OK, too).
Just a silly question: 54.Kd5? Ra8 55.Kc4 makes no sense. Why not 54.Kc4 at once? It still looks bad after 54...Ra8, but does not waste a move.
Anyway, your 55.Kc4 loses to 55...Ra7 with Rb7 to follow.
It seems we are speaking different languages.
I just said I would prefer 54. Kc4, as am lazy to calculate what happens in the other line.