Mesh stuff *could* work, but there is a good chance it will be janky. If cable isn't an option, then point-2-point wireless is the second best option. It's basically similar to mesh, but with (1) separate communication channel for "backhaul", i.e. from the shed to the house, and between the access point and the clients, i.e. inside the shed. Further, (2) you can have separate, directional antennas for the backhaul. I'm pretty sure you will be happy with that.
However if what you want is just to use YouTube and some music on your phone, why not just use mobile data? 4G / 5G is pretty good!
Mesh stuff *could* work, but there is a good chance it will be janky. If cable isn't an option, then point-2-point wireless is the second best option. It's basically similar to mesh, but with (1) separate communication channel for "backhaul", i.e. from the shed to the house, and between the access point and the clients, i.e. inside the shed. Further, (2) you can have separate, directional antennas for the backhaul. I'm pretty sure you will be happy with that.
However if what you want is just to use YouTube and some music on your phone, why not just use mobile data? 4G / 5G is pretty good!