Advocate IMAlviar ,
I raised a support ticket, and after much back & forth they acknowledged that it was a MSFT issue, that it was in the backlog to look at, but no ETA. (I literally shared the Snowflake ODBC Driver documentation with them to show them that this was a poor implementation of the driver on MSFTs part). I'm not convinced they actually believe this is an issue though, and just said that to get me to go away.
I also spoke with our account manager at MSFT, who just suggested we use Synapse - really helpful. I've also spoken to Snowflake to ask them to chase MSFT about it, but they don't seem interested either.
Solution Options;
1) Install the ODBC driver from Snowflake directly, setup a local DSN with that driver and (importantly) add the username_password_mfa parameter. Then in PowerBI, select ODBC, and point at that DSN. Not ideal, as it's a bit of messing around, and you lose the ability to do Direct Query (import only), but does resolve the MFA issue (which further demonstrates this is a MSFT issue)
2) Create your own Snowflake custom connector using the Power Query Connector SDK (https://learn.microsoft.com/en-us/power-query/install-sdk), and implement it correctly.
Our plan longer term is 2), but for now, we're doing 1) ... whilst also evaluating alternative BI platforms