Not everyone has a barbell, I know. But even doing the upright row with a broom handle will help with shoulder mobility. Honestly you can do an upright row with a rolled up towel.
You just gotta do it smart to not trash your shoulder. Jeff Nippard has good video on how to do it right and some other variations, while Jeff Cavalier has a good video explaining why the bad way is bad and some other variations.
But let’s talk to me and my far inferior state of video: