I’m encouraged to see the part about assessing options to maintain direct connectivity between Sheffield and Manchester Airport.
I take the point about passenger numbers being lower past Piccadilly but as someone who grew up in Sheffield I’d argue this link to the airport really is very important. I’ve used it many times myself - often on the very early morning trains, which would lead me to suggest that perhaps the earliest westbound departures i.e. the 5:09 and 6:09 could continue to serve the airport rather than Liverpool?
"Maintaining direct connectivity" is likely code for "keeping a handful of route retention trains", thereby killing two birds with one stone. That would probably mean the same as what runs in the current timetable (3 eastbound and 2 westbound trains, early and late in the day).
We had a couple of years of being the largest city in Europe without an airport until they tried to get rid of that embarrassment by telling us an old RAF airfield on the wrong side of Doncaster counted as an airport for Sheffield. Without a direct link to the airport that sense of being cut off will only grow - no family off on holiday will want to change trains with two or three 20kg hold luggage suitcases in tow.
Seeing as we're making European comparisons, I wonder if you could name many other cities the size of Sheffield that have a direct intercity-style train to a different city's airport? Frankfurt and Paris are the only examples I can think of. Almost all cities require you to take a metro-type service into the city centre, before changing to wherever you're going.
The point is, if you started developing a new timetable from a clean sheet, given the infrastructure that currently exists, there is no way that you would sensibly link Sheffield and Manchester Airport with a direct train. The fact that it even exists is purely because of historical quirks and political inertia - no politician wants to be seen as "that horrible guy that cut our airport link".