Launching a cell will make this message appear:
Connecting to kernel: Python 3.9.6 64-bit: Activating Python Environment 'Python 3.9.6 64-bit'
This message will then stay up loading indefinitely, without anything happening. No actual error message.
I've already tried searching for this problem, but every other post seem to obtain at least an error message, which isn't the case here. I still looked at some of these, which seemed to indicate the problem might have come from the traitlets package. I tried to downgrade it to what was recommended, but it didn't solve anything, so I reverted the downgrade.
The main problem here is that I have no idea what could cause such a problem, without even an error message.
Not sure what did the trick but downgrading VSCode to November version and after that reinstalling Jupyter extension worked for me.