I also had a rotator cuff injury that did not require surgery, only PT. As others recommended, I’d suggest a trainer for your bike. I picked up a good one on craigslist for cheap, put a slick on the rear of my old mountain bike and caught up on a lot of documentaries and podcasts while pedaling. One thing I found helpful was to swap out the low handlebars for some upright bars. Sure they don’t do much for the bike’s aesthetic, but it really reduced any additional reinjury when I got back on the road. I initially used really high bars called Nitto Bosco bars. Felt awkward being that upright but I was able to keep riding. Eventually moved down to a Nitto Albatross bar and then back to lower bars. Took about a year but it kept me riding as it healed.

Good luck with your recovery.
john