Looking at the Manchester situation:
How much might a Vic/Pic tunnel cost and My guess would be eywatering amounts, so why not sort Castlefield and Piccadilly 13/14 out properly with 4 tracking and possibly flying junctions outside Piccadilly to avoid conflicts across the main station throat. It isnt going to cost as much as a tunnel and addresses existing heavy rail problems. Create some West facing bays at Piccadilly in the triangle between Plats 13 and 12. This means that some services can terminate at Pic from the west.
Stage 2 then refurbish Victoria, make it a more pleasent place and try and get two more through platforms to the south of platform 3.
Stage 3 Convert the Bury line back to heavy rail or maybe tram train, and run into Piccadilly via Castlefield into west facing bays. Two advantages, you now have a proper regular Pic - Vic link with heavy rail, which is going to help people arriving into Vic from the NE and wanting the airport and the other connections Piccadilly offers, and you relieve the tram network of some of its load. If you wanted you could use tram-trains and run onwards from Pic rather than terminating there. An alternative would be to provide some West facing bays at Victoria and have a Victoria - Airport shuttle via Piccadilly and leave the Bury as a tram.
Yes it will take a bit longer than a direct tunnel for the Vic - Pic transfer, but will be more convenient than the current options which are tram or walk, as currently the heavy rail is an unreliable half hourly service between the two, pre covid, and this isnt adequate.
While sorting out Castlefield I would also combine and reduce to one station the current Deansgate - Manchester-O-R pair, they are only about 500m apart which is far too close and just creates further operational difficulties.