I got that email the other week, but I’d had 7. Only two down to wear, the others non-repairable punctures (according to KF). One of them got replaced and then got a puncture about 6 days later! Like you it coincided around the 16-20 week before end time so must be a degree of automation involved. I just deleted it and thought well I’ve still got one left then!
Same here it was simply an automated email which I read, deleted and thought no more of, the 8 tyres seemed a reasonable number (we are also on four).