Interaction between Adapt.jl and jacobian_ad

The `semi` itself is constructed with two arguments, `RealT` and `uEltype`, that determine the type of internal caches, etc. By default, they will be `Float64`, but there should be some clear interaction between all these types.

For example, how would you see the interaction with AD like in https://github.com/trixi-framework/Trixi.jl/blob/36dab43ad09975a27fe27958ab74f3b102898784/src/semidiscretization/semidiscretization.jl#L268-L278

_Originally posted by @ranocha in https://github.com/trixi-framework/Trixi.jl/pull/2212#discussion_r2203926581_