In 2008, Cad CTS had a compact spare, jack etc. available for about $300. Regarding its use on your car, check to see what the owner’s manual says and ask your dealer. If he does not know, there is nothing to prevent him from asking Cadillac.
We also have a car with no spare tire. We did get a puncture with a resulting slow leak while far from home. I took the tire off of the car, found and pulled out the puncturing object and inserted a rope plug to hold until we got home. If you do this, take note of the angle of the puncturing object so you can insert the rope plug in the same direction.
After arriving at home, the rope plug was removed and a mushroom plug was installed.
Be aware too that not all tire people will repair a puncture after the sealant has been used. I checked three places. Two would not; one would. If you can’t find someone to repair a tire with the sealant, you then get to buy a new tire. I am hoping that the lack of a spare tire will eventually be thought of as a bad idea that deserves to go away.