Generalize tests from JSOSolvers and add them here

If possible, we should try to move tests from JSOSolver and use them here. In particular, testing whether there are allocations is very useful.

Start by comparing the tests in JSOSolver with the tests already present here, paying particular attention to allocation checks. Determine which tests can be generalized for SolverTest.jl and define completion as having the relevant JSOSolver coverage available here, including useful allocation testing.

Written by the indexing model from the issue text.