As I found my attempt to answer last night quite embarrassing, I had to dig into this a little more.
I still I have not found any documentation, but I did some investigation. I get the impression that the FTData folder is created in the folder which you specify as the Data folder when you run Setup. This value is then found as HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Microsoft SQL Server\MSSQL15.INSTANCE\Setup\SqlDataRoot. (I made an installation where I set the data folder to be different from the other folders in the setup.) Note that this is not the same value that you see SSMS as the default data directory.
I assuming that you have this one located on the drive that is going away, and if my theory is correct, you would need to update this value. But I have not actually tested that this is the way to go.