Chris Webb has an update for us:
Some good news for those of you using DirectQuery mode in Power BI: the ApproximateDistinctCount DAX function, which returns an estimate of the number of the distinct values in a column and which can be a lot faster than a true distinct count as returned by the DistinctCount function, is now available to use with BigQuery, Databricks and Snowflake sources. It only worked with Azure SQL DB and Synapse before; RedShift is coming soon. You can use it in exactly the same way that you would with the DistinctCount function except that it only works in DirectQuery mode.
As always, there’s an example. I do wonder if the DAX function uses the same HyperLogLog algorithm that SQL Server uses for its approximate count distinct.