My Book Duo USB prevents functioning Mac keyboard & mouse on Boot

WD External and Portable SSD External SSD for macOS
1

I have a late-2013 27" iMac (Catalina 10.15.7) with four USB 3.0 ports:

  1. Apple Superdrive
  2. USB Stick
  3. My Passport
  4. My Book Duo
    Problem: If the My Book Duo external drive is connected to the Mac when powered up, my Apple wireless keyboard and Apple wireless mouse will not connect to the Mac (bluetooth). Makes no difference which port the My Book Duo is connected to. (No problems with the My Passport, btw).

It also makes no difference the My Book Duo is the only USB device connected. I have tried three different Apple wireless keyboards and two different Apple wired keyboards.

If I boot the Mac up with the My Book Duo USB cable disconnected and connect it after login, there is no problem. The My Book Duo has been attached to this Mac for 3 years without a problem.

Any ideas?

2

I have exactly the same problem and identical configuration (late-2013 27" iMac with Catalina 10.15.7and four USB 3.0). I cannot remind when the issue begun happening.
I use to boot from the internal SSD disk and it works fine only when I have just one single external USB drive connected. As soon as I plug 2 or more external USB drive, then the wireless Apple keyboard and mouse won’t be connected at the boot, so it is impossible to log in.
No idea so far… Hope you have found a solution you can share. Thanks