If you’ve installed PulseAudio, you may have not removed all of the packages properly.
As @grahamh has stated, Bluetooth audio streaming works out of the box now.
Hello Sam, seems like there is nothing left from Pulseaudio.
Still getting this message ‘ConditionPathIsDirectory=/sys/class/bluetooth was not met’ while starting the Bluetooth.
I’ve been searching around, and seems like it could be due to a H/W failure… several people reported this error message 
Should I try the OSMC Bluetooth dongle from the Store ? Is there a tutorial to install ? (I’d like to stream music through my USB output….connected to my audio DAC).
I’d try a fresh installation first – or using Raspberry Pi OS to confirm the possibility of hardware failure.
Can you connect to a WiFi hotspot? The WiFi / BT module are combined and if you can connect WiFi the module is likely functional as a whole.
Hello Sam, sorry for the belated reply (between holidays and family/kids sick, did not have much time 
)
I do not have any « wireless » option under Network when I click on OSMC via Kodi. Only « wired » and « MySQL » show up
Can I try something via the command ?
Thank you
Did you check if WiFi / BT is working through Raspberry Pi OS?
If it does – that will rule out a hardware failure
Sam
Please excuse my ignorance, but how do I proceed ?
Raspberry Pi OS is an operating system put out by the people who make the Raspberry Pi hardware (It used to be called Raspbian). Sam was suggesting that you install that OS to help you determine if your issue is with your OSMC install or if you have a hardware problem.
Hi there, me again 
I re-installed OSMC on a brand new SD, putting it back into my Rpi3.
Starting Bluetooth and check status sends back
Condition: start condition failed
Does this mean that my Bluetooth hardware is damaged ? Again I cannot see it under My OSMC > Network. I only see Wired and MySQL.
If your hadware is damaged, it won’t work under Raspberry Pi OS as suggested above. Did you try that?
I didn’t. What do I need to do ? install Raspberry OS instead of OSMC ?
Yes
Hello, I finally found the time to get a new SD and install Raspberry OS.
I’m not at all familiar with it.
How do I proceed to communicate with it per SSH ? And to check if the Bluetooth is working ?
Thanks a lot
You wouldn’t need SSH. You should have a full X11 GUI which then also would allow you to pair bluetooth