Remove `flux_viscous` temporary storage in `dg_2d_parabolic.jl`

If there is an easy way to remove the temporary storage, I suggest to give it a try - if not, record it for later.

_Originally posted by @sloede in https://github.com/trixi-framework/Trixi.jl/pull/1156#discussion_r940652018_

Right now, `flux_viscous` stores the viscous flux as a temporary variable for `TreeMesh` solvers. This can be removed if the interface terms involving `flux_viscous` could be computed on the fly instead.

Start by reading dg_2d_parabolic.jl and tracing how TreeMesh interface terms use the flux_viscous temporary storage. Determine whether those terms can be computed on the fly without changing the solver interface. Done means the temporary storage is removed safely; otherwise document why it must remain for later work.

Written by the indexing model from the issue text.