Welcome to FT
I called again, as the booking had appeared on my account statement, but I had only received the Avios, and not the Tier Points
In this instance, your flights flown on 05 November were not credited to your account until 13 November. As your Tier Point collection year was reset on 9 November, the 80 Tier Points for these flights were credited straight into your Lifetime Tier Point balance.
So your flights posted on the normal timeline I would expect. Usually BA flights post 3-7 days after the flight, which yours did. Flights taken just before your year end, but posting just after, will show as avios only and zero TPs. But as you have been advised, those TPs do add to your lifetime total. So far nothing unusual or worthy of complaint.
The actual problem is that those TPs should have helped add to your yearly total for your 9 Nov 2023 to 8 Nov 2024 membership year, and taken your total above 600 to get you silver status - for the purposes of this answer I am assuming you have done your 4 eligible flights as well. Now what you may need to do is prod BA to review this and manually change your status up to silver. This is not an unusual situation, it does happen quite a bit. I note you contacted CR, presumably via the online complaints form, but tbh this is not the best route to solving the issue. It also seems there was some confusion about your request/complaint anyway as their answer doesn't address the actual problem here, instead merely explaining what I noted above,
So before we start engaging in legal action, what you actually need to do is contact your exec club number by phone and ask them quite simply and briefly to send off a request to the back office to do this review and change. Do not start complaining about flights posting late or suggesting legal actions to the agent - it is unnecessary and unhelpful. Just say your flights posted just after year end, and those points should have got you silver, so it just needs to be manually checked now.