Data point -
Straight forward claim from June 2023 for delay out of Europe due to mechanical issue leading to overnight at LHR and 22 hour total delay from scheduled arrival to US, no response at 8 weeks including to an updated message I sent asking for any update. I submitted to CEDR at 8.5 weeks, they replied needing a bit more information at 2 more weeks, then at 4 weeks from CEDR claim got a reply from BA agreeing to full payment of 5 EU261 claims (2 adults, 2 ticketed children, 1 lap infant) and one night hotel/food/transit between LHR/hotel. Payment posted in another week about, so about 5-6 weeks from CEDR claim and 13-14 weeks from initial claim it is settled.

Thanks to all for the info here and hope others have similar success