BA recommend you go to the Qantas lounge for a few reasons. One of which, as aforementioned, is that it is close to the typical BA departure gates (6 and 7). The other being the agreement that has been made between the 2 airlines in terms of cost.

Why the check-in staff mention to not use The Pier (or The Wing) and only The Deck? Well the customer facing instruction is that it is closer to the gate, but it'll (almost certainly) be a cost factor involved too. Whilst it offers similar hard amenities (shower suites, noodle bar), its offerings are substantially less than The Pier in terms of the amount of food available (amongst other things) and therefore, a boarding pass scan at The Deck is much less than the equivalent thereof at The Pier. If members recall back in 2021 (or 2022...) when CX reopened their lounge at LHR T3 despite only have 1 (or not even any) flight operated by themselves per day. Despite agreements with airlines such as AA (when their lounge was closed), it could also get money from the BA passengers who entered the lounge.