Hello
Can i add a BIOS battery to a MikroTik router to help preserve the time settings when the device is powered off, similar to how a battery works in a computer?
No, none of MT devices have support for battery-backed real-time clock. Quite possibly the RTC support is stripped out of linux kernel, provided in ROS.
Use a proper UPS, perhaps ?
Usually, on PCs, RTC is in a separate chip.