Hi,
You may find it here:
https://www.stat.gov.tm/population-census
This is a page for the 2022 census and stats of Turkmen population in Turkmenistan. It's documents you have to download. The one the most important for us is the "1. ILATYŇ SANY WE ÝERLEŞIŞI." It references all lawfully recognized settlements and their "population," I used this documents to add a lot of settlements on the map using soviet maps, local sources and deduction as names change regularly and we're light years from what it was at the time of the Soviet union. I only add settlements I have no or little doubt about.
I also use this document for the population although it should be considered with a lot of precautions. This census has been widely criticized by external actors as not accurate and falsified to boost the numbers of the actual population of Turkmenistan, I still use it because it's the only recent official document existing.
If you have any question about it or how to use it let me know.