Well spotted, a trolley is actually en kärra (other words are en vagn and in Stockholm we say en pirra), but en väska is a bag or a case, like in suitcase. So no, the sentence doesn't refer to a luggage trolley that you put your suitcase on, it refers to a bag/case with wheels.
I am an elderly person. My younger brother gave me a Rolson (rolls on) but I did not use it for shopping until, one day, we took a dog to the vet and, while my wife stayed with the dog, I went round the corner to the supermarket. I didn't have the coin to release a trolley so I used my Rolson to collect the shopping, loaded it onto the till-belt + then back into the bag. The problem was when I got back to the car I couldn't lift it. so finished up decanting everything into several shopping bags. A complete waste of time!