If existing infrastructure is being used inefficiently, the number one priority is to make better use of it, and only then consider additional infrastructure.
The fundamental problems with Manchester' rail infrastructure are due to the down-sizing many years ago and understandable failure to anticipate the more recent (until Covid) increase in rail use. The number one mistake (viewed with a retrospectoscope) was the attempt to focus services on Piccadilly and the Castlefield line and slim down Victoria. Infrastructure improvements to the Castlefield line would be very expensive, partly as it is on a viaduct, which is presumably why the DfT/Treasury is baulking at the cost.
If an operational solution doesn't provide sufficient mitigation, the cheapest infrastructure solution is to build more capacity (e.g. extra sidings) to enable more long distance trains to terminate at Victoria, so that they can be removed from the Castlefield line (other than Liverpool to Sheffield via the CLC line). Releasing ex-GC platform capacity at Piccadilly by converting the Piccadilly-Reddish-Marple Rose Hill line to Metrolink would enable more Standedge line trains to terminate there, also relieving pressure on Victoria as well as the Castlefield line.