refactor: Convert *Problem constructors to accept SciMLProblemOptions

[AayushSabharwal]

Extends the SciMLFunctionOptions options-struct pattern (already applied to *Function constructors) down through DiscreteProblem, ImplicitDiscreteProblem, IntervalNonlinearProblem, DAEProblem, ODEProblem, SteadyStateProblem, SDEProblem, DDEProblem, SDDEProblem, NonlinearProblem, NonlinearLeastSquaresProblem, HomotopyProblem, OptimizationProblem, BVProblem, and LinearProblem: each now has a public (sys, op, tspan, opts::SciMLProblemOptions) entry point alongside its kwargs-based wrapper.

__process_SciMLProblem gains an options_struct = Val(true) mode that calls the target *Function's own opts-accepting method directly instead of its permissive kwargs wrapper, fixing a latent bug where a *Problem constructor naming a SciMLFunctionOptions field explicitly (e.g. sparse) would consume it out of the kwargs pass-through before it reached the inner *Function (concretely: LinearProblem(...; sparse = true) never reached LinearFunction). Since the opts-accepting methods have no such catch-all, bespoke keywords that used to ride through harmlessly (steady_state, seed, noise, constant_lags, checkvars, _skip_tstops, ...) are now explicitly intercepted at each call site and either discarded or re-merged into the final constructor call as needed.

Also: BVProblem now stores check_compatibility/t in the options struct itself (via a new shared maybe_derive_t_from_tspan helper) rather than as bespoke keywords; removes the unused cse keyword from HomotopyProblem; fixes constant_lags on DDEProblem/SDDEProblem to resolve symbolic parameter references against the built p instead of silently dropping them; and removes the now-unnecessary kwargs... from maybe_build_initialization_problem, closing off a path where bespoke keywords could leak into the initialization subproblem's own Function construction.

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

Add any other context about the problem here.

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Benchmark Results (Julia vlts)

Time benchmarks

	master	7912043...	master / 7912043...
ODEProblem	5.36 ± 0.18 ms	5.48 ± 0.25 ms	0.978 ± 0.056
init	0.068 ± 0.019 ms	0.0685 ± 0.018 ms	0.993 ± 0.39
large_parameter_init/ODEProblem	16.7 ± 0.79 ms	17.5 ± 0.82 ms	0.952 ± 0.064
large_parameter_init/init	0.0771 ± 0.024 ms	0.083 ± 0.023 ms	0.93 ± 0.38
mtkcompile	9.38 ± 0.32 ms	9.35 ± 0.42 ms	1 ± 0.056
sparse_analytical_jacobian/ODEProblem	19.1 ± 0.69 ms	19.2 ± 0.62 ms	0.993 ± 0.048
sparse_analytical_jacobian/f_iip	0.064 ± 0.001 μs	0.07 ± 0.001 μs	0.914 ± 0.019
sparse_analytical_jacobian/f_oop	0.376 ± 0.012 ms	0.379 ± 0.012 ms	0.992 ± 0.043
time_to_load	6.04 ± 0.071 s	6.05 ± 0.087 s	0.999 ± 0.019

Memory benchmarks

	master	7912043...	master / 7912043...
ODEProblem	0.0373 M allocs: 2.01 MB	0.0373 M allocs: 2.01 MB	1
init	0.433 k allocs: 0.0721 MB	0.433 k allocs: 0.0721 MB	1
large_parameter_init/ODEProblem	0.159 M allocs: 5.99 MB	0.159 M allocs: 5.99 MB	1
large_parameter_init/init	0.621 k allocs: 0.175 MB	0.621 k allocs: 0.175 MB	1
mtkcompile	0.059 M allocs: 3.34 MB	0.059 M allocs: 3.34 MB	1
sparse_analytical_jacobian/ODEProblem	0.115 M allocs: 5.55 MB	0.115 M allocs: 5.55 MB	1
sparse_analytical_jacobian/f_iip	0 allocs: 0 B	0 allocs: 0 B
sparse_analytical_jacobian/f_oop	0.634 k allocs: 19.6 kB	0.634 k allocs: 19.6 kB	1
time_to_load	0.153 k allocs: 14.5 kB	0.153 k allocs: 14.5 kB	1

[github-actions]

Benchmark Results (Julia v1)

Time benchmarks

	master	7912043...	master / 7912043...
ODEProblem	3.72 ± 0.13 ms	3.74 ± 0.14 ms	0.993 ± 0.051
init	0.0346 ± 0.017 ms	0.0344 ± 0.018 ms	1.01 ± 0.73
large_parameter_init/ODEProblem	11.3 ± 2 ms	11.7 ± 1.4 ms	0.961 ± 0.21
large_parameter_init/init	0.057 ± 0.032 ms	0.0557 ± 0.027 ms	1.02 ± 0.75
mtkcompile	6.19 ± 0.3 ms	6.29 ± 0.49 ms	0.983 ± 0.09
sparse_analytical_jacobian/ODEProblem	13.2 ± 1.5 ms	14.6 ± 1.6 ms	0.908 ± 0.14
sparse_analytical_jacobian/f_iip	0.081 ± 0.01 μs	0.061 ± 0.01 μs	1.33 ± 0.27
sparse_analytical_jacobian/f_oop	0.0924 ± 0.011 ms	0.0925 ± 0.011 ms	0.999 ± 0.17
time_to_load	4.89 ± 0.027 s	4.94 ± 0.045 s	0.991 ± 0.011

Memory benchmarks

	master	7912043...	master / 7912043...
ODEProblem	0.0363 M allocs: 1.66 MB	0.0363 M allocs: 1.64 MB	1.01
init	0.436 k allocs: 0.0542 MB	0.436 k allocs: 0.0542 MB	1
large_parameter_init/ODEProblem	0.151 M allocs: 4.95 MB	0.151 M allocs: 4.95 MB	1
large_parameter_init/init	0.819 k allocs: 0.154 MB	0.819 k allocs: 0.154 MB	1
mtkcompile	0.0559 M allocs: 2.6 MB	0.0559 M allocs: 2.6 MB	1
sparse_analytical_jacobian/ODEProblem	0.115 M allocs: 4.6 MB	0.115 M allocs: 4.6 MB	1
sparse_analytical_jacobian/f_iip	0 allocs: 0 B	0 allocs: 0 B
sparse_analytical_jacobian/f_oop	0.848 k allocs: 27 kB	0.848 k allocs: 27 kB	1
time_to_load	0.145 k allocs: 11 kB	0.145 k allocs: 11 kB	1