This fan problem persists as of July, 2023. I am also experience it.
Upon Mac shutdown, the R6 smaller fan continues to run. The only way I can make the fan stop is by disconnecting power from the R6. The R6 is using newest firmware dated 2023/04/11. If I eject the R6, then power the unit off prior to Mac shutdown the smaller fan will turn off, but the next time I start the Mac up, the R6 will NOT turn on automatically. I am connecting to the R6 via Thunderbolt and I am using an M2 Ultra Mac Pro, with OS 13.4.1
If there is anyone from Promise on this thread, can you tell us if the firmware will ever be updated to fix this problem? It's not a terrible inconvenience to eject the R6 before shutting down, but it seems odd that the unit won't turn back on automatically. In short: the unit is not acting as it is supposed to and that is worrisome.