Use proxy types that are passed to `P4estMesh` to allow to dispatch on the first argument?

This is more of a general remark. The `P4estMesh` has many different options of generating meshes: structured, INP, now cubed sphere. Possibly soon also `UnstructuredQuadMesh`. Instead of differentiating by the arguments to the constructor, what about using proxy types that are passed to `P4estMesh` that allows to dispatch on the first argument?

For example (names can/must be optimized),
* `Abaqus`
* `Structured`
* `CubedSphere`
Such that you could just call
```julia
P4estMesh(CubedSphere(3, 2, 0.5, 0.2), ...)
```

I am not sure if this needs to be done in this PR, I just wanted to put this out as an idea.

_Originally posted by @sloede in https://github.com/trixi-framework/Trixi.jl/pull/689#discussion_r662111889_