Improve Mosek interface to select optimal solution

[mgrabovsky]

Closes#665

Changes proposed in this Pull Request

Mosek can produce two distinct solutions with separate statuses: an interior-point solution (soltype.itr) and a basic solution (soltype.bas) obtained by basis identification (crossover).

Previously, linopy's Mosek interface only read the IPM solution. If the IPM terminated with solsta.dual_infeas_cer but crossover then recovered an optimal basic solution, linopy would report infeasible_or_unbounded with Objective: nan and the actual optimal solution would be silently discarded, even though Mosek itself had it.

After this change, linopy picks the solution (between bas, itr and itg) with the best score, with the order being solsta.[integer_]optimal > any other defined status > undefined. If both bas and itr are optimal, the itr solution is chosen to preserve backward compatibility with the previous behavior.

This patch was co-authored with Claude Opus 4.7.

Checklist

• Code changes are sufficiently documented; i.e. new functions contain docstrings and further explanations may be given in doc.
• Unit tests for new features were added (if applicable).
• A note for the release notes doc/release_notes.rst of the upcoming release is included.
• I consent to the release of this PR's code under the MIT license.

[FabianHofmann]

@mgrabovsky thanks for the pr, this is unfortunately something that has to wait for #628 after which this needs a rebase. happy to help at this later point in time.

[mgrabovsky]

@FabianHofmann I've rebased the PR on top of master now. Could you please check if it looks good?

[FBumann]

@mgrabovsky thanks for your PR. It looks quite focused. As i dont use mosek, i cant really replicate the issue, but I had a look and i would suggest the following changes:

1. move _choose_mosek_solution to Mosek._choose_solution() as a staticmethod, as its clearly scoped there
2. Dont bypass _make_result(), so self.status, self.solution & Result.solver_name are populated

[mgrabovsky]

Thanks for the review and tips. I've updated the PR.

[FabianHofmann]

looks good, happy to merge after we slightly refactor the tests for maintaining the structure and not bloat the set of flat functions