Like @Milliways wrote, You should be able to power a USB hard disk from the Pi3B+ but it really depends on the drive (and the PSU of the Pi).
Also, if the files you are working on are important, I suggest you to use a powered usb hub to prevent "bad things" from happening.
"My guess is that RPI-4 can't handle 2 usb powered disks. Both disks
are fine, but the logs say there are problems."
Your guess is correct. This is something that appears regularly on Raspberry Pi forums. The Rpi 4, like the other models, can supply 1.2 A total to all USB ports. That is, the maximum is shared. Most USB 'portable' type USB powered drives ...