Fix deprecation and method redefinition warnings in CI tests

[ChrisRackauckas-Claude]

Summary

• Rename overwritten function definitions to unique names in test files to eliminate WARNING: Method definition overwritten messages (7 files)
• Add local keyword to disambiguate soft scope assignments in test loops and @test_broken blocks (4 files)
• Replace deprecated ModelingToolkit APIs: ODESystem → System, NonlinearSystem → System, structural_simplify → mtkcompile
• Replace deprecated sol[end] indexing with sol.u[end] for RecursiveArrayTools compatibility
• Fix function signatures (add missing p parameter) that were previously hidden by method accumulation on shared f generic

Details

Method redefinition warnings fixed

These test files defined multiple functions named f with different signatures, causing WARNING: Method definition f(...) overwritten messages in CI:

• test/problem_creation_tests.jl — renamed to f_ode, f_2ndorder, f_sde, g_sde, f_dae, f_rode, f_discrete, f_steady
• test/forwarddiff_dual_detection.jl — renamed to f_nlsolve, f_1021
• test/downstream/solve_error_handling.jl — renamed to f_oop, f_iip, f_sde
• test/downstream/community_callback_tests.jl — renamed to collision_affect!, terminate_affect!
• test/downstream/distributed_ensemble.jl — renamed to simple_prob_func, lorenz_prob_func

Soft scope warnings fixed

• test/downstream/kwarg_warn.jl — removed unnecessary sol = assignment in @test_throws
• test/downstream/solve_error_handling.jl — added local in for loop, removed unnecessary assignment
• test/downstream/null_de.jl — added local in for loop
• test/downstream/default_linsolve_structure.jl — added local in @test_broken blocks

Deprecated API replacements

• test/downstream/null_de.jl — ODESystem → System, NonlinearSystem → System, structural_simplify → mtkcompile
• test/downstream/subarray_support.jl — sol[end] → sol.u[end]

Test plan

• Core tests pass locally with --depwarn=yes
• No method redefinition warnings remain in core tests
• Runic formatting check passes on all changed files
• CI should pass on all test groups

🤖 Generated with Claude Code