FYI, this is a super frequently asked question (at least once a day). So you can see lots more discussion by searching the subreddit.
In general, though, the current thinking is that you don’t need to stress about eating protein right after a workout in order to build muscle. As long as you are getting enough protein overall, your body will know when to use it to build muscle.
This also goes for carbs. Your body will pull from its stored fuel (glycogen stored in liver and muscles, as well as fat) as needed to fuel a workout. You may not be able to achieve quite the same sprint speed while fasting, or one-rep max quite as high while fasting, as you could if you carb-loaded beforehand. But your goal is to lose weight and get stronger, not to win a competition every day. You’re still getting those benefits, even if your “fasting personal best” is a bit below your “carb-loaded personal best.”
TL;DR As long as you feel OK while working out fasted (not dizzy, sick, bad pain, or super-weak), then you are not hurting your body at all.
Obviously listen to your body (if it really hurts, if you feel faint, etc!), but plenty of folks myself included exercise in the midst of fasts. I regularly run 5-8 miles 20+ hours into a fast without issue, and have been for the past 6 months.
Daily protein intake, anywhere from 0.8-1.0+ gram per pound depending on activity and goals, is mostly what matters. It’s not like the body shuts off trying to repair itself just because it didn’t get a protein shake within 30 minutes of a workout. My two cents is that everything else is just grinding out those last few percentages - and some of it is just fitness industry nonsense - and matters for folks training for like the Olympics.
If your current method is working well for you, I see no reason to change it.