ENH: Improve solver and adjoint testing (in a systematic way)

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Improve the solver and adjoint testing framework, with hollistic while simple and systematic tests. a minima

• internal state fluxes and outputs validation on reference test cases
• adjoint validation*
• also Bayesian specifi tests required?
• ...

Define semi analytical cases? Benchmark basis with runs from other reference codes on our cases and data?

[inoelloc]

We need to improve our test framework with different levels of testing depending of the changes applied to the code base.