So in 4E 174 the Thalmor sacked and burned the Imperial city during the Great War. Is there any indication of what happened to the Temple of the One or that statue of Akatosh and is it safe to say they perished as well?

As far as I know, there's no documentation of that.

If them pointy ears lay a hand on that monument of my homie Martin Imma be having Altmer shishkebabs for tonight