They haven't stopped but they don't happen immediately.
replyDetailed census records are published 72 years after they were collected; the last release (of 1950 census data) came out in 2022; the next one should be published in 2032.
They didn't stop publishing census data. Its publication is delayed for approximately one human lifetime, to avoid affecting the living:
replyhttps://prologue.blogs.archives.gov/2022/01/20/census-record...
The Census Bureau is a lot more than the 10-year Census, and it already makes very extensive use of IRS data and other administrative sources. Virtually everything that is published using these sources uses either differential privacy or other privacy protection methods that are prohibited by the order. I'm guessing that a lot of those pieces of data are just going to be put on hold until the order is reversed or weakened. A number of things might have to go away permanently, as there's almost certainly no way to protect privacy in them without some kind of noise infusion.
replyTBH I don't think the people who wrote this knew how much collateral impact it would have.