Great progress on your muscle up and handstand my friend, keep it up! As for the back lever, heh, it’s really hard. When you do skin the cat are you actually doing it for reps like lower down pull back lower down etc or simply hanging at the bottom? You should be doing it for reps to most effectively build strength. When you get to the bottom try to “relax” in it (keep your arms and shoulders engaged, but let your body “sink” to a low point to maximize your gains. At the bottom you should feel a stretch in your chest). Also, keep your legs straight throughout the movement.
Besides that, getting better at muscle ups will only help your back lever. Elbow levers will actually teach you the proper body positioning for a back lever. Also, you should be very strong at pull ups and dips, probably also pretty good at handstand push ups (with a wall) before you can do a back lever. Getting good at the L sit wouldn’t hurt either, especially for the core strength.