Reinstalled it, but it doesn't work, and icon doesn't appear on the top dock
You might need to run
sudo modprobe btusb on the command line if you uninstalled and disabled the kernel module.
For example running
sudo lsmod | grep blue gives me the result:
bluetooth 540672 41 btrtl,hci_uart,btintel,btqca,bnep,btbcm,rfcomm,btusb ecdh_generic 24576 1 bluetooth
You can check if you have the above kernel modules available, and if not, you might need them, depending on your hardware setup.
You can disable them again with
sudo modprobe -r btusb as an example. Let me know if you get it working. It can be quite fiddly and sometimes I need to remove
btusb and add it again to revive bluetooth after standby (not always), and if bluetooth is completely failing, you often need to shutdown and power off completely, not just restart to revive it.