I am pretty sure it has closed now,and moved to Stafford archives,which is virtually next door.
I don't think it has closed.
https://www.staffordshire.gov.uk/Heritage.../williamsalt/home.aspxLichfield Record Office (just a few miles away from Stafford), HAS now closed.
It used to hold all the wills for the Diocese of Lichfield, (copies of which are on findmypast on film, but if you want to see the 'real thing', they are now at Stafford), plus many other documents.
All these have now moved to Staffordshire Record Office.
As you say, Staffordshire Record Office and The William Salt Library are very close indeed - one backs on to the other.