After the battle between Ancano and the Arch-Mage Savos Aren, I've found Mirabelle Ervine and Ancano are also walking around as if nothing has happened, although Mirabelle Ervine dialogue does continue as normal telling you to get on your feet. Gather your wits. Tell her you feel ok, and she will tell you that Ancano is doing something with the Eye of Magnus and that the Arch-Mage is missing.

Once her dialogue finishes and you need to find Savos Aren, for me he appears in the College of Winterhold as if he's just limped in from the main door, crawling about and not being able to interact with him.

Console commands for MG05 and mg06 don't work, I can only get the quest to progress with MG07 but that itself causes issues where I am not recognised as the Arch-Mage.

I've found MG05 and mg06 in the Creation Kit, I've simply used the tick box to mark them both as complete at index 200, set the Next Quest as mg06 and MG07 and created the mod using Mod Organiser, it is set at the bottom of my load order.

Going back into Skyrim everything seems to be fixed, I've checked the dialogue and actions that are meant to occur in MG05 and mg06 and the game follows what is meant to happen as far as I can observe.

I hope this is a potential fix for everyone still playing Skyrim, however, if this does not fix the issue for you or you simply want to fix it for yourself in the Creation Kit, here is where I found MG05 and mg06:
Character - Quest - Faction - Mages Guild (The first option as there are 2 options in my Creation Kit with the title Mages Guild, the first option for me has no additional tree, the second option has an additional tree called Radiant).

Hopefully this all makes sense or the file I have uploaded fixes the issue for you.