So I talked to a very helpful person on Apple Support. It turns out they were defective and Apple is kindly sending me a new set.
In case this helps someone else, this is what I learned, to trouble shoot:
Make sure you have the latest firmware (currently 3.7.2) for the Beats Flex and the latest iOS (14.2) on your device. in the Bluetooth setting, “forget” and then re-pair your Beats Flex if you needed to update either.
If the headphones still aren’t sounding ok, reset them - hold the power button and the volume down button for 15 seconds. The power LED light will blink red. Let go of the buttons. On your iPhone etc, “forget” the Beats Flex in the Bluetooth setting and then re-pair them to your device.
If the sound is still all muffled and it seems like your mic is picking up every move and rustle the cord makes, they are defective.