I see this is your third post. Welcome to the forum.
STAFFORD BYPASS
A Stafford bypass would work well, but it needs to include a bypass of Colwich Junction too, which is the more limiting constraint on WCML capacity.
In my opinion, the cheapest way to do this would be to continue the HS2 mainline from Fradley Junction for 18km to Great Haywood, and then build a chord to merge onto the line from Colwich to Stoke at Hixon. That would permith 4tph from HS2 to access Manchester by using the paths through South Manchester currently used by two Avanti and two Cross-County services each hour. To make this work, the Manchester-Stoke stopper would need to be extended to Birmingham to serve Wolverhampton-Manchester traffic.
Taking HS2 further, past Stafford and thus completing a Stafford bypass, would only add more capacity if the new design for Euston station enables enough HS2 trains to make use of it. The best place to merge onto the WCML would be around Baldwin's Gate, where HS2 could join the fast lines. This is another 25km of HS2 mainline.
4-tracking Crewe to Preston as a cheaper/better option than extending HS2 to Crewe.
It's not an either - or. If HS2 doesn't get past Colwich, then there will no more trains coming up the WCML than there are at present. You need to bypass Colwich somehow to get any benefit from upgrading Crewe to Preston.
HS2 TO HIXON
If HS2 gets to Hixon, then everything going up to Stoke comes from HS2, and Colwich no longer operates as a flat junction with the crossing moves that severely limit capacity. Instead, it becomes a place where the WCML funnels down from four tracks to two, with no crossing moves. So the capacity of Colwich immediately increases from say 8tph to around 12tph.
These extra 4tph on the WCML can probably get through Crewe station, but the rail network south of Manchester has no more capacity, given it is already carrying the HS2 4tph through Hixon and Stoke, and the WCML from Crewe to Weaver Junction is at capacity now. So there is nowhere for extra traffic to go. (Except for more freights heading for the yards just south of Crewe.)
At this point is becomes worth four-tracking Crewe-Weaver. That could be very easily done and would add at least 10tph to the capacity of this section. The alignment is wide enough through Winsford, and many of the modern bridges on that line (e.g. A54, Acton Bridge, A556) were constructed to accommodate four tracks already. So this could be done at relatively low cost. The main requirement would be to move Acton Bridge and Hartford stations, which block any widening, and replace them by a new station at Weaverham where the WCML is already four tracks wide. For details see this thread:
https://www.railforums.co.uk/threads/four-tracking-crewe-to-weaver-junction.268735/
HS2 TO BALDWINS GATE
If Great Haywood to Baldwins Gate was built, and Euston had the capacity, then HS2 could deliver up to 12tph to Crewe on the fast lines. The slow lines from Stafford could carry perhaps 8tph, being a mix of freights and traffic from Birmingham. This is far more traffic than the WCML currently carries between Stafford and Crewe, and at the moment there is nowhere for it to go. I don't know how many tph Crewe Station can handle. It might need a lot of rebuilding to take much more than it does now.
North of Weaver Junction, the WCML is a mess. Sometimes four tracks; sometimes two. The slow lines swap from east of the fasts to the west, and back again - all on the flat.
I don't think it would be possible to four track the line through Preston Brook, so you'd have to tunnel under Preston-on-the-Hill, or build a chord to connect the WCML slows onto the Manchester-Chester line near Frodsham. That would give you four tracks all the way to Winwick junction, just south of Newton-le-Willows. You'd have to raise the bridge over the underpass at Warrington Bank Quay to get the down (northbound) slow back onto the West side of the fasts
(or swap the slows and fasts around to keep both slows on the East side).
Newton-le-Willows is a mess too. The Up (southbound) slow crosses the fasts on the flat at Winwick, only for the slow route to cross over the mainline and rejoin it from the East side at Golborne Junction. At which point the slow again cross the fasts on the flat to the West side of the alignment.
What might be needed is to quadruple the fasts on the direct line between Winwick and Golborne junctions. This looks feasible, but building directly alongside a working railway is dangerous and expensive. A two-track bypass route might be better.
There is also a need for a high speed route from the WCML from Crewe onto the Chat Moss route towards Manchester. The Chat Moss is the only route through the suburbs of Manchester that is not fully congested and could feasibly carry extra HS2 trains from London to Manchester without building the £17bn HS2 tunnel past the airport.
(Personally I'd knock down the AO Arena at Manchester Victoria and build 400m-long platforms there, with 400m reversing sidings at Rochdale, but that's beyond the scope of this thread.)
North of Newton, it's four tracks to Wigan and then only two to Euxton Balshaw Lane where it reverts to four to Preston. It doesn't look like it would be easy to quad these, so getting four tracks all the way to Preston might require a new line. But it may not be needed. The most important destination by far for HS2 is Manchester. Any increased capacity between Crewe and Newton-le-Willows should firstly be used to get more HS2 trains to Manchester via Chat Moss.
I hope this is helpful. You might find
https://www.openrailwaymap.org/ useful for showing details of track layout and junction names.