In a rational world the high speed service would give a cross platform interchange with the fast/semi-fast service at Crewe, with both trains timed to be there at same time, so can connect to North Wales, and those from Midlands connect to trains going north.
At moment there is no provisional published timescale, so can't tell if a change (even via bridge/subway) at Crewe is few minutes, or nearer an hour. (A similar query has previously come up about changing at Old Oak Common from South West, again could be minutes, or nearly hours wait for connection). No one seems to know yet.
There is a difference between the two.
Based on the full plan, at Crewe there would be 2tph to London, along with 2tph to Liverpool and 1tph to Lancaster. (Apparently you can only go to places beginning with L ... so just Llandudno, not Holyhead any more

). The vast majority of passengers connecting onto HS2 from the NWML would be wanting trains to London, so you could sensibly time that connection.
But at Old Oak Common, there would be trains every 5 minutes or so, all going to different northern destinations. So any one train coming in from the West Country will have good connections to
some HS2 destinations but not to others, and it's just the luck of the draw if your train has good connections to Liverpool but not to Leeds which it is that you want to go to.
But with only half a dozen stations on the full plan scheduled to get an hourly service, the vast majority of passengers would have a connection time of no more than 30 minutes.