This does strike me as all rather poor.
I used the perfectly pleasant (no luxury, but very respectable f&b options) TLL lounge last month, when departing on Norra to HEL for my onward connection to BA. Extremely courteous lounge personnel (well ..... there was just one !)
There were about four other pax using the reasonably spacious lounge at the time. Norra is a subsidiary of Finnair, a OW member of course, operating code-shares with BA.
Is this lack of any arrangement for BA premium cabin travellers really anything other than a money-saving measure .....?
As an aside - there is a rather pleasant-looking coffee/patisserie type shop in the main concourse, with a stylish layout and comfy chairs. You might want to give it a try, OP.