Since fastboot works, maybe try to fastboot boot into recovery (from file on PC), I don’t see how, fastboot would work if it was a hardware issue, maybe just software, maybe try different recoveries.
As I mentions before, fastboot works fine. ADB sideload does not work neither with LOS-Recovery nor TWRP. Also ADB does not work if the FP3 ist booted into LOS and USB-Debugging is enabled within the developer options.
I assume a broken bottom module (e.g. broken soldering, resistor, …) or defektive main/core module.
Today I received 2 brand new bottom modules for FP3. One of them I installed for testing purposes into the FP3 we are talking about here. And voila: It’s fully functional again.
I recommend using USB-cable of top brands (e.g. Anker) and if you are struggling with USB-issues first change the cable and second the bottom module, which isn’t too expensive.