Add the adjoint_tests LFRic App to the integration testing

[arporter]

Recently we introduced a bug to PSyAD that wasn't caught until the MO tested with the latest PSyclone. Now that LFRic Apps has the adjoint_tests App, we could extend the integration tests to build and run it. Can you foresee any problems with that @DrTVockerodtMO (i.e. additional dependencies etc.)?

[arporter]

I think we want to wait to do this until we move all of the LFRic integration testing up to the new (1.2?) release of LFRic Apps. @TeranIvy might have a view too.

[DrTVockerodtMO]

I think with the new release cycle as opposed to just versioning it seems doable. Note that previously discussions were held where the adjoint is permitted to be broken (i.e.: fail the LFRic tests) for a time whilst we endeavour to fix it. So there could be a situation where the LFRic integration tests in PSyclone expectedly fail through no fault of PSyclone itself.

In my (limited) experience I have been fast enough on tickets such that I can fix the adjoint_tests app during that ticket's life cycle but there is provision at least for it to be broken for more time, hopefully not between two different versions I would think but I am not sure. Could be tricky!

[arporter]

Thanks @DrTVockerodtMO. We don't update our LFRic environment very often so I think we could just choose a version where PSyAD is known to work?