Out of curiosity, have you tried extended arm hangs? Believe I read that hanging helps with shoulder impingement.
This link references the concept and supposedly the science behind it, but I haven’t read it closely: https://www.onebed.com.au/eliminate-shoulder-pain-with-a-simple-and-easy-exercise/
There hasn’t been much scientific research on this topic and what has been done is on, of course, rodents. However, the limited research does suggest that fasting can help rehabilitate injuries. It is by no means certain; it looks promising. However, doing fasting for a long as you want is not a good idea because of protein catabolism. Fasting for injury repair should really be 3-5 days, maximum.
As for weightlifting that is OK so long as it is light and low, just enough, as you say, to keep active. This is not the time to be trying to build muscle by working out to fatigue. Working out too hard is going to make your problems worse.
My tendons feel at their best when I’m fasting. I go to the gym and lift weights during a fast and can really notice an improvement when fasted. Makes sence due to less inflammation. Food causes inflammation, especially junk food and carbs