@oriolmirosa this sounds like a cool extension! Unofortunately, we don’t have an easy way to track this at the moment. You could watch on changes to the cell metadata for the finished timing key to be added, but this will only be activated when the user enables recording cell timing (https://github.com/jupyterlab/jupyterlab/pull/7578#issuecomment-561792168)
If you are OK with also recording the timing into the users notebooks, your extension could enable this setting when it is registered.
If you don’t want to however, you would have to snoop on the kernel messages. I don’t know off the top of my head how to do this, but if you need help on this approach I can do some digging.