DLC and other problems with services Steam Origin (Mirror's Edge)

Posony, help me out.

The license of the game was bought both in Steam and in Origin + on PS3 and was handed out for free, I grabbed it. I play mainly through Steam, and, accordingly, I downloaded the game through it. But Origin easily detects game files from the root of Steam and can also run them.

Now to the question itself: DLC (time trial cards) are available for purchase only on Origin, in Steam they are not at all. If I buy this add-on on Origin, it will, in theory, be downloaded to the root folder of the game. it is in the Steam folder, then it will be possible to play through it? In principle, I don’t want to play through Origin.

Or do you altogether differently: take DLC on the third curling iron and not take a steam bath? (oddly enough, it's cheaper on PSN than on Origin).

I would be grateful for help or sensible advice.