The subway from Tennants Brewery to the stables on Castle Green is discussed in this thread:
In May 1939 there was a proposal to convert the subway/cellar into the main control centre for the ARP authorities at a cost of £2,000. The Home Office had vetoed the use of the basements under the Albert Hall. By September 1939 the cost had increased by £500 and award of the contract to W.G.Robson Ltd was imminent. By 1950 the subway was being used by Tennants as an area to fill casks.
Your post = CASTLE GREEN - May 16 2020 - has interesting info, along with the nice photograph.
There are some photos on PICTURE SHEFFIELD, and copies of some plans that mention Castle Green, the codes are:- arc03168 - arc03169 - arc04078 Regards Heartshome.
There is a bit of a write-up by 'FRIENDS of the OLD TOWN HALL, Castle Green' maybe something in that.
Or you could try asking 'FRIENDS of SHEFFIELD CASTLE' they seem to have maps/knowledge of the area.