|I have no idea what you should see on a Galaxy smartphone - but you know what to expect from your equipment and that is good enough for what we need.
I just checked with my MacBook Air and AirPods Pro on a Lightning/USB-C cable, the only place I could see the AirPods was in Settings/Bluetooth. With the case closed it offered the option Connect, and connected to show charge levels with the charging case opened.
If you are not getting that with your MacBook I think you have tried all the obvious home solutions. The next stage is probably to get your AirPods and charging case checked by Apple or authorised Apple service provider (depends on where you live around the world). Link https://getsupport.apple.com/ should help you find suitable hands-on service.