I am not convinced that the double TP offers have very much to do with how busy the lounges are. People who are getting silver status through BA holidays double TP offers are by and large travelling in cabins that would give GC access anyway and then probably not travelling much outside those bookings.

The more likely issue in my estimate is the number of Golds who have dropped to Silver (due to decreased flying and the expiry of status extensions, and work policy changes (as per OP)), combined with a return to travel for business travellers who are already at Silver status level and maintain it normally, a decrease in frequency of flights leading to a longer time spent in lounges waiting for connections, and BA selling out fairly massive CE cabins on a regular basis.