Transcend hard drive not showing up since updating to Mojave

If they are all bus-powered and not mounting, can you hear them spinning up. When they don't get enough power, you can often hear them spin up for a second or two, then it sounds like it is restarting the spin-up process over and over.

I have had external bus-powered hard drives from many different manufacturers. Many of them will start over-driving the USB ports requiring more power than can be supplied. They work fine for a while, but then start failing like that. However, I don't believe you'd see all of them behave that way all at once.

Given that the light usually indicates drive activity, I don't think this is it, but in the Finder if you Go > Computer, do you see the drives.

I would suggest using a powered USB3 hub from a well respected brand to connect the drives to the computer. The drives can use the extra power supplied by the powered hub. Plus the hub can insulate the drives from the Mac.

Try resetting the SMC on your Macs.

How to reset the System Management Controller (SMC) on your Mac - Apple Support

Are the hard drives bus-powered, or do they have a separate power source?

Are the drives formatted NTFS (Windows) and you have installed software to make them work on a Mac?

That software often fails when there is an update, and sometimes the failure results in blocking the mounting of drives.

Make sure this checkbox is checked:

Sometimes preferences get changed with big upgrades.