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Lots of "ifs" there...The main engine and generators will have cut out as soon as the heel angle reached 20 degrees.
She is heeling mainly because of the free surface effect of the water in her hold, which started to get in when the thrusters carried under deck parted their lashings and punched a hole in the side shell plating.
The usual approach will be to get a party aboard the derelict, get a light line to them, try to follow that with a messenger (you can see the problem - no power on the casualty - no power to her winches - no means of heaving in the messenger - one trick here is to take a light messenger round a heavy block and back to the tug, so as she steams away she hauls up the heavy messenger and then hauls the towing connection in). The towing connection can be prepared with wire tails to turn up on the casualty’s bitts.
Assuming all goes well the tug gets the casualty head to wind and you try to get portable pumps and portable generators aboard the casualty. If you can do that then you try to get water out of the hold and that will eventually bring her more upright.
At that point you try to make for shelter. A port may refuse her(*) until she is upright and you have got a patch on the hole.
Of course, she may decide to sink before you have got this lot done. In which case the boarding party will have to step off smartly, and you gave no cure, so no pay.