How do I navigate to Bluetooth settings when Mac mini mouse stops working

I keep a second AA-cell powered Bluetooth mouse on hand and paired for such situations. For the keyboard, if you plug it in to a USB port it will work as a wired keyboard until you can fix whatever the BT problem is.

Although I'm aware of Chrome computers, I have no practical experience with using them. As such, I can't verify whether or not, you can simply unpair the Logitech keyboard/mouse and switch it to your mini.

Also, Logitech has two options for wireless connectivity:

1. Bluetooth (as you're doing presently), and
2. With either a Logi Bolt (newer) or Unifying (older) USB receiver.

The statement I provided you earlier is for option two.

You should buy a cheap wired keyboard and mouse to keep on hand for just such emergencies. They are available in places like Amazon for about $20. You can probably pick something up at your local Best Buy as well.

If the other wireless devices are Bluetooth and already paired to another Mac, unfortunately, they won’t just work on your Mac mini without unpairing and re-pairing them manually. And without a working mouse or keyboard, that's hard to do. Apple doesn’t allow Bluetooth devices to switch Macs seamlessly like AirPods do—there’s no built-in multi-device pairing memory for most Apple mice/keyboards.

Of course, I'm assuming that you have both an Apple wireless keyboard and mouse for either Mac. If you're using a Logitech wireless mouse or keyboard with a USB Unifying Receiver, that’s a different story—they may work immediately if the dongle is plugged into the Mac mini.