Upvote:9
The first of your two options are not possible I think. It's all corridors without anwyhere to pause or anything to sit on, and I suspect if you attempted it you may be moved on by security.
Baggage claim may be possible, there's normally very little staff activity in the area.
Landside has limited facilities, but there are areas of seating in most departure areas before security. There's also several hotels on site, and if you are staying in Manchester, it's a fairly short journey to the city centre, and a "private hire" cab jourmey would typically cost you Β£25-Β£30. The "first" train after a 2AM arrival is not that long away, tomorrow for example there is an 03:59 departure.
I think there may also be some seating in the "skybridge" section above the station, or nearby, but I can't find photos to confirm.