So there are two separate issues and a couple of fog factors.
First issue, bags delayed, the majority of which arrived the next evening. To be fair, that's quite a good result for delayed bags. Vital medication in delayed bags, can't really blame the airline for that.
Second and more serious issue is theft from the baggage, a small bag with a belt and skin care products worth £500. That is presumably what you are complaining about the delay in the response?
Fog factors, Dad's 74th birthday and majorly stressful arrival in Larnaca. Statistically, one in 365 passengers on average would have a birthday the day you flew. With an average of 100,000 departing passengers daily, 274 would have had birthdays. Of course we don't know how many of those had delayed bags. No details provided about the majorly stressful arrival in Larnaca so unable to comment on whether BA responsible.
BA or your insurance will presumably adjudicate the claim, which is the only real issue. Not sure I'd be anticipating any avios.