That said, if you just want to know what proportion of the population has delta, you don't need to sequence that many cases. The point of sequencing a large fraction of cases is to catch emerging variants, that wouldn't be likely to be caught otherwise. But to know whether Delta is 30%, 50%, or 70% of cases, you just need a good random sample, not a particularly large one, and I imagine you can do that at the labs where the PCR tests are being run.
(at one point, I recall that the UK had a test that matched on three distinct sites on the virus, and they found that one of those sites would turn up negative for a particular variant, so they were able to use that as a proxy for the spread of the variant. I don't remember if that was Alpha or Delta though, and obviously it's no replacement for sequencing)
[0] https://cen.acs.org/analytical-chemistry/sequencing/200000-c...
[1] https://www.gov.uk/government/news/uk-exceeds-600000-covid-1...
US does statistical sampling and also prevents patients from being told about variants, https://news.ycombinator.com/item?id=28419280
https://www.cdc.gov/coronavirus/2019-ncov/variants/variant-s...
https://www.cdc.gov/coronavirus/2019-ncov/variants/cdc-role-...
If the lab finds that 87% of the samples from Adam's College are of the Omega Mu strain, then it's assumed 87% of total cases at Adam's College to be Omega Mu variant.
See page [pdf] 5 on this: https://www.doh.wa.gov/Portals/1/Documents/1600/coronavirus/...
It is updated every Wednesday
I've been watching the delta variant take over the world over the past several months here: https://covariants.org
(dark green is delta)
There is also a way to differentiate on some RT-PCR tests (but not all), depending on how they are made.