Choice of second-order AD and warnings

This issue is about the machinery for choosing backends and throwing warnings:

https://github.com/SciML/OptimizationBase.jl/blob/2ffab7e93197c1fc8d9ed6a39857e301a71a474e/src/adtypes.jl#L222-L236

https://github.com/SciML/OptimizationBase.jl/blob/2ffab7e93197c1fc8d9ed6a39857e301a71a474e/src/cache.jl#L45-L58

I think that this could be both optimized and simplified due to recent changes in DI.

Nowadays, DI.inner and DI.outer can also be called on backends which are not SecondOrder, they just act as the identity. Thus, you don't need to explicitly create a SecondOrder(adtype, adtype). Passing adtype alone will be equivalent in most cases, and faster in some because it can leverage custom Hessian implementations within a single backend (e.g. SecondOrder(AutoForwardDiff(), AutoForwardDiff()) cannot call ForwardDiff.hessian whereas AutoForwardDiff() can).
Furthermore, DI's hvp and hessian for AutoZygote() already use ForwardDiff-over-Zygote.

Here are my suggestions:

• Simplify the generate_adtype logic and its variants to avoid creating SecondOrder objects altogether.
• Throw a warning based on the modes DI.inner and DI.outer, e.g. when the inner backend is not a reverse mode backend. This can be checked with ADTypes.mode(DI.inner(adtype)) isa Union{ADTypes.ReverseMode,ADTypes.ForwardOrReverseMode}. Of course you also want to allow ForwardDiff so feel free to refine.
• Document this behavior so that users are less confused by the warnings (see this Discourse thread).

What do you think @Vaibhavdixit02?

Start with src/adtypes.jl lines 222-236 and src/cache.jl lines 45-58, then read the linked DifferentiationInterface inner, outer, hvp, and hessian behavior. Compare the current generate_adtype variants with the proposed mode-based warning logic. Done means the backend selection is simplified, warnings reflect the selected modes, and the behavior is documented for users.