You are being wildly optimistic if you think 1/3 of the population have natural immunity. Only in the worst hit areas is it that high.
The Wuhan Wild Type had a much lower R0. The math could work for herd immunity with that. Not with Delta and worse...
You won't ever hit herd immunity with a R0 of ~7 until you have true immunity of 85-90% or more for the entire population, and there would still be clusters due to uneven distribution of immunity in the population. You will never achieve that with a Ve of 88% and only 75% of the population eligible for vaccination and 15-50% of them unwilling.
The Pandemic ends when the prevalence vs consequences decrease to the levels of a bad seasonal influenza, and then we will say COVID is an endemic (seasonal respiratory virus) instead of pandemic illness.