So you are looking for an iPhone 11 Pro case that does more than just protecting your phone? The mophie Juice Pack Access battery case fits the bill. It adds additional battery juice, so you can use your phone all day. It also gives you full access to the Lightning port.
This battery case offers an additional 13 hours of audio and 5 hours of video. It has rubberized support pads to protect your phone from drops and falls. You can charge it with a Qi wireless charging pad or USB-C connection. Costs under $65 at the time of this writing.[where to get it]