For the common law, I think they always ask for common law/marriage proof regardless, even if the person it is not accompanying you in the application. I called IRCC and they told me that even If my partner doesn't not apply with me(and therefore could not be sponsored in the future) it should be added to the application and all the pertinent documents with it, as it could be a "grave" violation. Maybe to scare me, but one never knows with these things.
Well, they are right - you suppose to mention your common-law, you can't hide this thing.
The question is about "proof". Usually, they ask about proof because they need to issue PR for your partner, that's why you need to prove to them that this relationship is real.
In case your partner in Canadain, you can't be his/her sponsor, it's ridiculous and you are applying as a worker, so no need to prove the relationship, because you don't get any benefit from your partner. It's not a family reunion.
That's why I don't understand what's going on.