Avoid repeated code

As the number of set of equations we are able to solve increases, some code is repeated and could be easily avoided. As an example for the baroclinic test case the initial conditions and auxiliary functions are repeated, as they are written in terms of primitive variables. See for example [cartesian_to_sphere in Euler Energy](https://github.com/trixi-framework/TrixiAtmo.jl/blob/main/examples/elixir_euler_energy_baroclinic_instability.jl#L126C1-L135C4) [cartesian_to_sphere in Potential Temperature](https://github.com/trixi-framework/TrixiAtmo.jl/blob/main/examples/elixir_euler_potential_temperature_baroclinic_instability.jl#L125C1-L134C4) The same applies to source terms and initial conditions, which partially relates this issue also to [#120].