This is so simple, especially for software driven component! You should be able to set a sleep timer in Mosaic and/or it should power down if no music is playing for 60 min or something. Don’t tell me there’s a sleep function in Roon, don’t use this.
There is a sleep function on Bartok. Press the front panel power button once and it goes to sleep ( standby). However you are correct, there isn’t a sleep timer in Mosaic.
I am wondering what you want to achieve. If it is, for example, saving power then I doubt you will achieve much by putting Bartok or any DCS product into sleep mode as it more or less seems only to stop the device reacting to commands and turns off the OLED display. Power saving is small. In fact in their review of Rossini Hi-Fi News were unable to measure any saving at all. Otherwise the device remains on so as to preserve the correct internal temperature so that it is almost instantly ready for use when woken.
In regard to leaving it on, here is dCS on the subject: