Does arm motion stop at the same place in therapy, or can the therapist push it further passively? It would be nice if it was a matter of just stretching and loosening a muscle. You are still pretty early at 6 weeks, so some hope there. I thought I would have to learn to use my left (rightie here) hand to brush teeth while healing, but I found propping my right elbow on the counter and bending over the sink did a better job than awkward brushing with the left. You are probably taller than I am, so that may not be comfortable for you. It did take longer to get certain rotational motion back with the TSR arm, such as soaping up your body in the shower. I could get the range of motion, but my circular movements were very slow for the first couple of months, so I tended to use the off hand. A few years prior to surgery, I developed a frozen shoulder, there was no pain, but I could not lift my hand above ear level, could not comb or shampoo my hair or pick up heavy objects one handed. Then had PT which gave me about 80% of my range back. But then the next year I started to develop constant arthritis pains and again lost my range of motion, but this time it was with pain, x-rays showed bone on bone, so time for the TSR.
I hope your PT person can be of help in figuring out what they did in surgery and coming up with a plan to increase your range of movement. The PT guy I have seen for both my knees and my shoulder regularly sits in to view ortho surgeries a few times a year, it was interesting to hear him describe the operations from different view point.