Up until May of last year, there was a possibility of picking up BBC Radio Sheffield in Liverpool from its medium wave transmitter on 1035 MHz. (Even then, reception would have been weak and probably plagued by interference). However the station's medium wave transmitter is no longer in use.
There's not a cat in hell's chance of picking up signals from their VHF transmitters in Sheffield, Chesterfield and Doncaster, except on the very rare occasions that the atmospheric conditions result in what radio amateurs refer to as a 'lift' (which occurs only a few times a year and for only a few hours at s time).
As Liverpool is out of range of the Emley Moor transmitter mast, there's no chance of getting the station via Freeview either.
The DAB transmitters hosting BBC Radio Sheffield among their 'multiplexes' (= bundles of channels) are located close to Rotherham, Barnsley and Retford, with none of them being capable of reception in Liverpool.
BBC local radio stations aren't hosted on the satellites providing Freesat or Sky services.
So, as you've suggested in your post, Cleoval, that only leaves online reception via BBC Sounds. However you're not limited to only using your laptop. If you regularly want access to the station, your best option might be to use an Amazon Echo smart speaker (available from £39.99) or a Google Home one (from £49):
https://www.bbc.co.uk/usingthebbc/account/the-bbc-on-voice-devices/